Enter a problem...
Trigonometry Examples
,
Step 1
Step 1.1
Subtract from both sides of the equation.
Step 1.2
Multiply both sides of the equation by .
Step 1.3
Simplify both sides of the equation.
Step 1.3.1
Simplify the left side.
Step 1.3.1.1
Cancel the common factor of .
Step 1.3.1.1.1
Cancel the common factor.
Step 1.3.1.1.2
Rewrite the expression.
Step 1.3.2
Simplify the right side.
Step 1.3.2.1
Simplify .
Step 1.3.2.1.1
Apply the distributive property.
Step 1.3.2.1.2
Multiply by .
Step 1.3.2.1.3
Multiply .
Step 1.3.2.1.3.1
Multiply by .
Step 1.3.2.1.3.2
Combine and .
Step 1.3.2.1.4
Move the negative in front of the fraction.
Step 1.4
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 1.5
Simplify .
Step 1.5.1
Write the expression using exponents.
Step 1.5.1.1
Rewrite as .
Step 1.5.1.2
Rewrite as .
Step 1.5.2
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 1.5.3
To write as a fraction with a common denominator, multiply by .
Step 1.5.4
Combine and .
Step 1.5.5
Combine the numerators over the common denominator.
Step 1.5.6
Factor out of .
Step 1.5.6.1
Factor out of .
Step 1.5.6.2
Factor out of .
Step 1.5.6.3
Factor out of .
Step 1.5.7
To write as a fraction with a common denominator, multiply by .
Step 1.5.8
Combine and .
Step 1.5.9
Combine the numerators over the common denominator.
Step 1.5.10
Factor out of .
Step 1.5.10.1
Factor out of .
Step 1.5.10.2
Factor out of .
Step 1.5.10.3
Factor out of .
Step 1.5.11
Multiply by .
Step 1.5.12
Multiply.
Step 1.5.12.1
Multiply by .
Step 1.5.12.2
Multiply by .
Step 1.5.13
Rewrite as .
Step 1.5.13.1
Factor the perfect power out of .
Step 1.5.13.2
Factor the perfect power out of .
Step 1.5.13.3
Rearrange the fraction .
Step 1.5.14
Pull terms out from under the radical.
Step 1.5.15
Combine and .
Step 1.6
The complete solution is the result of both the positive and negative portions of the solution.
Step 1.6.1
First, use the positive value of the to find the first solution.
Step 1.6.2
Next, use the negative value of the to find the second solution.
Step 1.6.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 2
Step 2.1
Replace all occurrences of with in each equation.
Step 2.1.1
Replace all occurrences of in with .
Step 2.1.2
Simplify the left side.
Step 2.1.2.1
Simplify .
Step 2.1.2.1.1
Simplify each term.
Step 2.1.2.1.1.1
Simplify the numerator.
Step 2.1.2.1.1.1.1
Apply the product rule to .
Step 2.1.2.1.1.1.2
Simplify the numerator.
Step 2.1.2.1.1.1.2.1
Apply the product rule to .
Step 2.1.2.1.1.1.2.2
Raise to the power of .
Step 2.1.2.1.1.1.2.3
Rewrite as .
Step 2.1.2.1.1.1.2.3.1
Use to rewrite as .
Step 2.1.2.1.1.1.2.3.2
Apply the power rule and multiply exponents, .
Step 2.1.2.1.1.1.2.3.3
Combine and .
Step 2.1.2.1.1.1.2.3.4
Cancel the common factor of .
Step 2.1.2.1.1.1.2.3.4.1
Cancel the common factor.
Step 2.1.2.1.1.1.2.3.4.2
Rewrite the expression.
Step 2.1.2.1.1.1.2.3.5
Simplify.
Step 2.1.2.1.1.1.2.4
Expand using the FOIL Method.
Step 2.1.2.1.1.1.2.4.1
Apply the distributive property.
Step 2.1.2.1.1.1.2.4.2
Apply the distributive property.
Step 2.1.2.1.1.1.2.4.3
Apply the distributive property.
Step 2.1.2.1.1.1.2.5
Simplify and combine like terms.
Step 2.1.2.1.1.1.2.5.1
Simplify each term.
Step 2.1.2.1.1.1.2.5.1.1
Multiply by .
Step 2.1.2.1.1.1.2.5.1.2
Multiply by .
Step 2.1.2.1.1.1.2.5.1.3
Move to the left of .
Step 2.1.2.1.1.1.2.5.1.4
Rewrite using the commutative property of multiplication.
Step 2.1.2.1.1.1.2.5.1.5
Multiply by by adding the exponents.
Step 2.1.2.1.1.1.2.5.1.5.1
Move .
Step 2.1.2.1.1.1.2.5.1.5.2
Multiply by .
Step 2.1.2.1.1.1.2.5.2
Add and .
Step 2.1.2.1.1.1.2.5.3
Add and .
Step 2.1.2.1.1.1.2.6
Rewrite as .
Step 2.1.2.1.1.1.2.7
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 2.1.2.1.1.1.3
Raise to the power of .
Step 2.1.2.1.1.2
Multiply the numerator by the reciprocal of the denominator.
Step 2.1.2.1.1.3
Multiply .
Step 2.1.2.1.1.3.1
Multiply by .
Step 2.1.2.1.1.3.2
Multiply by .
Step 2.1.2.1.2
To write as a fraction with a common denominator, multiply by .
Step 2.1.2.1.3
To write as a fraction with a common denominator, multiply by .
Step 2.1.2.1.4
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Step 2.1.2.1.4.1
Multiply by .
Step 2.1.2.1.4.2
Multiply by .
Step 2.1.2.1.4.3
Multiply by .
Step 2.1.2.1.4.4
Multiply by .
Step 2.1.2.1.5
Combine the numerators over the common denominator.
Step 2.1.2.1.6
Simplify the numerator.
Step 2.1.2.1.6.1
Apply the distributive property.
Step 2.1.2.1.6.2
Multiply by .
Step 2.1.2.1.6.3
Expand using the FOIL Method.
Step 2.1.2.1.6.3.1
Apply the distributive property.
Step 2.1.2.1.6.3.2
Apply the distributive property.
Step 2.1.2.1.6.3.3
Apply the distributive property.
Step 2.1.2.1.6.4
Simplify and combine like terms.
Step 2.1.2.1.6.4.1
Simplify each term.
Step 2.1.2.1.6.4.1.1
Multiply by .
Step 2.1.2.1.6.4.1.2
Multiply by .
Step 2.1.2.1.6.4.1.3
Multiply by .
Step 2.1.2.1.6.4.1.4
Rewrite using the commutative property of multiplication.
Step 2.1.2.1.6.4.1.5
Multiply by by adding the exponents.
Step 2.1.2.1.6.4.1.5.1
Move .
Step 2.1.2.1.6.4.1.5.2
Multiply by .
Step 2.1.2.1.6.4.1.6
Multiply by .
Step 2.1.2.1.6.4.2
Add and .
Step 2.1.2.1.6.4.3
Add and .
Step 2.1.2.1.6.5
Apply the distributive property.
Step 2.1.2.1.6.6
Multiply by .
Step 2.1.2.1.6.7
Multiply by .
Step 2.1.2.1.6.8
Move to the left of .
Step 2.1.2.1.6.9
Add and .
Step 2.2
Solve for in .
Step 2.2.1
Multiply both sides by .
Step 2.2.2
Simplify.
Step 2.2.2.1
Simplify the left side.
Step 2.2.2.1.1
Simplify .
Step 2.2.2.1.1.1
Cancel the common factor of .
Step 2.2.2.1.1.1.1
Cancel the common factor.
Step 2.2.2.1.1.1.2
Rewrite the expression.
Step 2.2.2.1.1.2
Reorder and .
Step 2.2.2.2
Simplify the right side.
Step 2.2.2.2.1
Multiply by .
Step 2.2.3
Solve for .
Step 2.2.3.1
Move all terms not containing to the right side of the equation.
Step 2.2.3.1.1
Subtract from both sides of the equation.
Step 2.2.3.1.2
Subtract from .
Step 2.2.3.2
Divide each term in by and simplify.
Step 2.2.3.2.1
Divide each term in by .
Step 2.2.3.2.2
Simplify the left side.
Step 2.2.3.2.2.1
Cancel the common factor of .
Step 2.2.3.2.2.1.1
Cancel the common factor.
Step 2.2.3.2.2.1.2
Divide by .
Step 2.2.3.2.3
Simplify the right side.
Step 2.2.3.2.3.1
Cancel the common factor of and .
Step 2.2.3.2.3.1.1
Factor out of .
Step 2.2.3.2.3.1.2
Cancel the common factors.
Step 2.2.3.2.3.1.2.1
Factor out of .
Step 2.2.3.2.3.1.2.2
Cancel the common factor.
Step 2.2.3.2.3.1.2.3
Rewrite the expression.
Step 2.2.3.3
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 2.2.3.4
Simplify .
Step 2.2.3.4.1
Rewrite as .
Step 2.2.3.4.2
Simplify the numerator.
Step 2.2.3.4.2.1
Rewrite as .
Step 2.2.3.4.2.2
Pull terms out from under the radical, assuming positive real numbers.
Step 2.2.3.4.3
Multiply by .
Step 2.2.3.4.4
Combine and simplify the denominator.
Step 2.2.3.4.4.1
Multiply by .
Step 2.2.3.4.4.2
Raise to the power of .
Step 2.2.3.4.4.3
Raise to the power of .
Step 2.2.3.4.4.4
Use the power rule to combine exponents.
Step 2.2.3.4.4.5
Add and .
Step 2.2.3.4.4.6
Rewrite as .
Step 2.2.3.4.4.6.1
Use to rewrite as .
Step 2.2.3.4.4.6.2
Apply the power rule and multiply exponents, .
Step 2.2.3.4.4.6.3
Combine and .
Step 2.2.3.4.4.6.4
Cancel the common factor of .
Step 2.2.3.4.4.6.4.1
Cancel the common factor.
Step 2.2.3.4.4.6.4.2
Rewrite the expression.
Step 2.2.3.4.4.6.5
Evaluate the exponent.
Step 2.2.3.5
The complete solution is the result of both the positive and negative portions of the solution.
Step 2.2.3.5.1
First, use the positive value of the to find the first solution.
Step 2.2.3.5.2
Next, use the negative value of the to find the second solution.
Step 2.2.3.5.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 2.3
Replace all occurrences of with in each equation.
Step 2.3.1
Replace all occurrences of in with .
Step 2.3.2
Simplify .
Step 2.3.2.1
Simplify the left side.
Step 2.3.2.1.1
Remove parentheses.
Step 2.3.2.2
Simplify the right side.
Step 2.3.2.2.1
Simplify .
Step 2.3.2.2.1.1
Simplify the numerator.
Step 2.3.2.2.1.1.1
To write as a fraction with a common denominator, multiply by .
Step 2.3.2.2.1.1.2
Combine and .
Step 2.3.2.2.1.1.3
Combine the numerators over the common denominator.
Step 2.3.2.2.1.1.4
Multiply by .
Step 2.3.2.2.1.1.5
To write as a fraction with a common denominator, multiply by .
Step 2.3.2.2.1.1.6
Combine and .
Step 2.3.2.2.1.1.7
Combine the numerators over the common denominator.
Step 2.3.2.2.1.1.8
Multiply by .
Step 2.3.2.2.1.1.9
Multiply by .
Step 2.3.2.2.1.1.10
Simplify the numerator.
Step 2.3.2.2.1.1.10.1
Expand using the FOIL Method.
Step 2.3.2.2.1.1.10.1.1
Apply the distributive property.
Step 2.3.2.2.1.1.10.1.2
Apply the distributive property.
Step 2.3.2.2.1.1.10.1.3
Apply the distributive property.
Step 2.3.2.2.1.1.10.2
Simplify and combine like terms.
Step 2.3.2.2.1.1.10.2.1
Simplify each term.
Step 2.3.2.2.1.1.10.2.1.1
Multiply by .
Step 2.3.2.2.1.1.10.2.1.2
Multiply by .
Step 2.3.2.2.1.1.10.2.1.3
Multiply by .
Step 2.3.2.2.1.1.10.2.1.4
Multiply .
Step 2.3.2.2.1.1.10.2.1.4.1
Multiply by .
Step 2.3.2.2.1.1.10.2.1.4.2
Raise to the power of .
Step 2.3.2.2.1.1.10.2.1.4.3
Raise to the power of .
Step 2.3.2.2.1.1.10.2.1.4.4
Use the power rule to combine exponents.
Step 2.3.2.2.1.1.10.2.1.4.5
Add and .
Step 2.3.2.2.1.1.10.2.1.5
Rewrite as .
Step 2.3.2.2.1.1.10.2.1.5.1
Use to rewrite as .
Step 2.3.2.2.1.1.10.2.1.5.2
Apply the power rule and multiply exponents, .
Step 2.3.2.2.1.1.10.2.1.5.3
Combine and .
Step 2.3.2.2.1.1.10.2.1.5.4
Cancel the common factor of .
Step 2.3.2.2.1.1.10.2.1.5.4.1
Cancel the common factor.
Step 2.3.2.2.1.1.10.2.1.5.4.2
Rewrite the expression.
Step 2.3.2.2.1.1.10.2.1.5.5
Evaluate the exponent.
Step 2.3.2.2.1.1.10.2.1.6
Multiply by .
Step 2.3.2.2.1.1.10.2.2
Subtract from .
Step 2.3.2.2.1.1.10.2.3
Add and .
Step 2.3.2.2.1.1.10.2.4
Add and .
Step 2.3.2.2.1.1.11
Multiply by .
Step 2.3.2.2.1.1.12
Cancel the common factor of and .
Step 2.3.2.2.1.1.12.1
Factor out of .
Step 2.3.2.2.1.1.12.2
Cancel the common factors.
Step 2.3.2.2.1.1.12.2.1
Factor out of .
Step 2.3.2.2.1.1.12.2.2
Cancel the common factor.
Step 2.3.2.2.1.1.12.2.3
Rewrite the expression.
Step 2.3.2.2.1.1.13
Rewrite as .
Step 2.3.2.2.1.1.14
Simplify the numerator.
Step 2.3.2.2.1.1.14.1
Rewrite as .
Step 2.3.2.2.1.1.14.2
Pull terms out from under the radical, assuming positive real numbers.
Step 2.3.2.2.1.1.15
Multiply by .
Step 2.3.2.2.1.1.16
Combine and simplify the denominator.
Step 2.3.2.2.1.1.16.1
Multiply by .
Step 2.3.2.2.1.1.16.2
Raise to the power of .
Step 2.3.2.2.1.1.16.3
Raise to the power of .
Step 2.3.2.2.1.1.16.4
Use the power rule to combine exponents.
Step 2.3.2.2.1.1.16.5
Add and .
Step 2.3.2.2.1.1.16.6
Rewrite as .
Step 2.3.2.2.1.1.16.6.1
Use to rewrite as .
Step 2.3.2.2.1.1.16.6.2
Apply the power rule and multiply exponents, .
Step 2.3.2.2.1.1.16.6.3
Combine and .
Step 2.3.2.2.1.1.16.6.4
Cancel the common factor of .
Step 2.3.2.2.1.1.16.6.4.1
Cancel the common factor.
Step 2.3.2.2.1.1.16.6.4.2
Rewrite the expression.
Step 2.3.2.2.1.1.16.6.5
Evaluate the exponent.
Step 2.3.2.2.1.2
Combine and .
Step 2.3.2.2.1.3
Multiply by .
Step 2.3.2.2.1.4
Multiply the numerator by the reciprocal of the denominator.
Step 2.3.2.2.1.5
Cancel the common factor of .
Step 2.3.2.2.1.5.1
Factor out of .
Step 2.3.2.2.1.5.2
Cancel the common factor.
Step 2.3.2.2.1.5.3
Rewrite the expression.
Step 2.4
Replace all occurrences of with in each equation.
Step 2.4.1
Replace all occurrences of in with .
Step 2.4.2
Simplify .
Step 2.4.2.1
Simplify the left side.
Step 2.4.2.1.1
Remove parentheses.
Step 2.4.2.2
Simplify the right side.
Step 2.4.2.2.1
Simplify .
Step 2.4.2.2.1.1
Simplify the numerator.
Step 2.4.2.2.1.1.1
To write as a fraction with a common denominator, multiply by .
Step 2.4.2.2.1.1.2
Combine and .
Step 2.4.2.2.1.1.3
Combine the numerators over the common denominator.
Step 2.4.2.2.1.1.4
Multiply by .
Step 2.4.2.2.1.1.5
Multiply .
Step 2.4.2.2.1.1.5.1
Multiply by .
Step 2.4.2.2.1.1.5.2
Multiply by .
Step 2.4.2.2.1.1.6
To write as a fraction with a common denominator, multiply by .
Step 2.4.2.2.1.1.7
Combine and .
Step 2.4.2.2.1.1.8
Combine the numerators over the common denominator.
Step 2.4.2.2.1.1.9
Multiply by .
Step 2.4.2.2.1.1.10
Multiply by .
Step 2.4.2.2.1.1.11
Simplify the numerator.
Step 2.4.2.2.1.1.11.1
Expand using the FOIL Method.
Step 2.4.2.2.1.1.11.1.1
Apply the distributive property.
Step 2.4.2.2.1.1.11.1.2
Apply the distributive property.
Step 2.4.2.2.1.1.11.1.3
Apply the distributive property.
Step 2.4.2.2.1.1.11.2
Simplify and combine like terms.
Step 2.4.2.2.1.1.11.2.1
Simplify each term.
Step 2.4.2.2.1.1.11.2.1.1
Multiply by .
Step 2.4.2.2.1.1.11.2.1.2
Multiply by .
Step 2.4.2.2.1.1.11.2.1.3
Multiply by .
Step 2.4.2.2.1.1.11.2.1.4
Multiply .
Step 2.4.2.2.1.1.11.2.1.4.1
Multiply by .
Step 2.4.2.2.1.1.11.2.1.4.2
Raise to the power of .
Step 2.4.2.2.1.1.11.2.1.4.3
Raise to the power of .
Step 2.4.2.2.1.1.11.2.1.4.4
Use the power rule to combine exponents.
Step 2.4.2.2.1.1.11.2.1.4.5
Add and .
Step 2.4.2.2.1.1.11.2.1.5
Rewrite as .
Step 2.4.2.2.1.1.11.2.1.5.1
Use to rewrite as .
Step 2.4.2.2.1.1.11.2.1.5.2
Apply the power rule and multiply exponents, .
Step 2.4.2.2.1.1.11.2.1.5.3
Combine and .
Step 2.4.2.2.1.1.11.2.1.5.4
Cancel the common factor of .
Step 2.4.2.2.1.1.11.2.1.5.4.1
Cancel the common factor.
Step 2.4.2.2.1.1.11.2.1.5.4.2
Rewrite the expression.
Step 2.4.2.2.1.1.11.2.1.5.5
Evaluate the exponent.
Step 2.4.2.2.1.1.11.2.1.6
Multiply by .
Step 2.4.2.2.1.1.11.2.2
Subtract from .
Step 2.4.2.2.1.1.11.2.3
Subtract from .
Step 2.4.2.2.1.1.11.2.4
Add and .
Step 2.4.2.2.1.1.12
Multiply by .
Step 2.4.2.2.1.1.13
Cancel the common factor of and .
Step 2.4.2.2.1.1.13.1
Factor out of .
Step 2.4.2.2.1.1.13.2
Cancel the common factors.
Step 2.4.2.2.1.1.13.2.1
Factor out of .
Step 2.4.2.2.1.1.13.2.2
Cancel the common factor.
Step 2.4.2.2.1.1.13.2.3
Rewrite the expression.
Step 2.4.2.2.1.1.14
Rewrite as .
Step 2.4.2.2.1.1.15
Simplify the numerator.
Step 2.4.2.2.1.1.15.1
Rewrite as .
Step 2.4.2.2.1.1.15.2
Pull terms out from under the radical, assuming positive real numbers.
Step 2.4.2.2.1.1.16
Multiply by .
Step 2.4.2.2.1.1.17
Combine and simplify the denominator.
Step 2.4.2.2.1.1.17.1
Multiply by .
Step 2.4.2.2.1.1.17.2
Raise to the power of .
Step 2.4.2.2.1.1.17.3
Raise to the power of .
Step 2.4.2.2.1.1.17.4
Use the power rule to combine exponents.
Step 2.4.2.2.1.1.17.5
Add and .
Step 2.4.2.2.1.1.17.6
Rewrite as .
Step 2.4.2.2.1.1.17.6.1
Use to rewrite as .
Step 2.4.2.2.1.1.17.6.2
Apply the power rule and multiply exponents, .
Step 2.4.2.2.1.1.17.6.3
Combine and .
Step 2.4.2.2.1.1.17.6.4
Cancel the common factor of .
Step 2.4.2.2.1.1.17.6.4.1
Cancel the common factor.
Step 2.4.2.2.1.1.17.6.4.2
Rewrite the expression.
Step 2.4.2.2.1.1.17.6.5
Evaluate the exponent.
Step 2.4.2.2.1.2
Combine and .
Step 2.4.2.2.1.3
Multiply by .
Step 2.4.2.2.1.4
Multiply the numerator by the reciprocal of the denominator.
Step 2.4.2.2.1.5
Cancel the common factor of .
Step 2.4.2.2.1.5.1
Factor out of .
Step 2.4.2.2.1.5.2
Cancel the common factor.
Step 2.4.2.2.1.5.3
Rewrite the expression.
Step 3
Step 3.1
Replace all occurrences of with in each equation.
Step 3.1.1
Replace all occurrences of in with .
Step 3.1.2
Simplify the left side.
Step 3.1.2.1
Simplify .
Step 3.1.2.1.1
Simplify each term.
Step 3.1.2.1.1.1
Simplify the numerator.
Step 3.1.2.1.1.1.1
Apply the product rule to .
Step 3.1.2.1.1.1.2
Raise to the power of .
Step 3.1.2.1.1.1.3
Use the power rule to distribute the exponent.
Step 3.1.2.1.1.1.3.1
Apply the product rule to .
Step 3.1.2.1.1.1.3.2
Apply the product rule to .
Step 3.1.2.1.1.1.4
Simplify the numerator.
Step 3.1.2.1.1.1.4.1
Raise to the power of .
Step 3.1.2.1.1.1.4.2
Rewrite as .
Step 3.1.2.1.1.1.4.2.1
Use to rewrite as .
Step 3.1.2.1.1.1.4.2.2
Apply the power rule and multiply exponents, .
Step 3.1.2.1.1.1.4.2.3
Combine and .
Step 3.1.2.1.1.1.4.2.4
Cancel the common factor of .
Step 3.1.2.1.1.1.4.2.4.1
Cancel the common factor.
Step 3.1.2.1.1.1.4.2.4.2
Rewrite the expression.
Step 3.1.2.1.1.1.4.2.5
Simplify.
Step 3.1.2.1.1.1.4.3
Expand using the FOIL Method.
Step 3.1.2.1.1.1.4.3.1
Apply the distributive property.
Step 3.1.2.1.1.1.4.3.2
Apply the distributive property.
Step 3.1.2.1.1.1.4.3.3
Apply the distributive property.
Step 3.1.2.1.1.1.4.4
Simplify and combine like terms.
Step 3.1.2.1.1.1.4.4.1
Simplify each term.
Step 3.1.2.1.1.1.4.4.1.1
Multiply by .
Step 3.1.2.1.1.1.4.4.1.2
Multiply by .
Step 3.1.2.1.1.1.4.4.1.3
Move to the left of .
Step 3.1.2.1.1.1.4.4.1.4
Rewrite using the commutative property of multiplication.
Step 3.1.2.1.1.1.4.4.1.5
Multiply by by adding the exponents.
Step 3.1.2.1.1.1.4.4.1.5.1
Move .
Step 3.1.2.1.1.1.4.4.1.5.2
Multiply by .
Step 3.1.2.1.1.1.4.4.2
Add and .
Step 3.1.2.1.1.1.4.4.3
Add and .
Step 3.1.2.1.1.1.4.5
Rewrite as .
Step 3.1.2.1.1.1.4.6
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 3.1.2.1.1.1.5
Raise to the power of .
Step 3.1.2.1.1.1.6
Multiply by .
Step 3.1.2.1.1.2
Multiply the numerator by the reciprocal of the denominator.
Step 3.1.2.1.1.3
Multiply .
Step 3.1.2.1.1.3.1
Multiply by .
Step 3.1.2.1.1.3.2
Multiply by .
Step 3.1.2.1.2
To write as a fraction with a common denominator, multiply by .
Step 3.1.2.1.3
To write as a fraction with a common denominator, multiply by .
Step 3.1.2.1.4
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Step 3.1.2.1.4.1
Multiply by .
Step 3.1.2.1.4.2
Multiply by .
Step 3.1.2.1.4.3
Multiply by .
Step 3.1.2.1.4.4
Multiply by .
Step 3.1.2.1.5
Combine the numerators over the common denominator.
Step 3.1.2.1.6
Simplify the numerator.
Step 3.1.2.1.6.1
Apply the distributive property.
Step 3.1.2.1.6.2
Multiply by .
Step 3.1.2.1.6.3
Expand using the FOIL Method.
Step 3.1.2.1.6.3.1
Apply the distributive property.
Step 3.1.2.1.6.3.2
Apply the distributive property.
Step 3.1.2.1.6.3.3
Apply the distributive property.
Step 3.1.2.1.6.4
Simplify and combine like terms.
Step 3.1.2.1.6.4.1
Simplify each term.
Step 3.1.2.1.6.4.1.1
Multiply by .
Step 3.1.2.1.6.4.1.2
Multiply by .
Step 3.1.2.1.6.4.1.3
Multiply by .
Step 3.1.2.1.6.4.1.4
Rewrite using the commutative property of multiplication.
Step 3.1.2.1.6.4.1.5
Multiply by by adding the exponents.
Step 3.1.2.1.6.4.1.5.1
Move .
Step 3.1.2.1.6.4.1.5.2
Multiply by .
Step 3.1.2.1.6.4.1.6
Multiply by .
Step 3.1.2.1.6.4.2
Add and .
Step 3.1.2.1.6.4.3
Add and .
Step 3.1.2.1.6.5
Apply the distributive property.
Step 3.1.2.1.6.6
Multiply by .
Step 3.1.2.1.6.7
Multiply by .
Step 3.1.2.1.6.8
Move to the left of .
Step 3.1.2.1.6.9
Add and .
Step 3.2
Solve for in .
Step 3.2.1
Multiply both sides by .
Step 3.2.2
Simplify.
Step 3.2.2.1
Simplify the left side.
Step 3.2.2.1.1
Simplify .
Step 3.2.2.1.1.1
Cancel the common factor of .
Step 3.2.2.1.1.1.1
Cancel the common factor.
Step 3.2.2.1.1.1.2
Rewrite the expression.
Step 3.2.2.1.1.2
Reorder and .
Step 3.2.2.2
Simplify the right side.
Step 3.2.2.2.1
Multiply by .
Step 3.2.3
Solve for .
Step 3.2.3.1
Move all terms not containing to the right side of the equation.
Step 3.2.3.1.1
Subtract from both sides of the equation.
Step 3.2.3.1.2
Subtract from .
Step 3.2.3.2
Divide each term in by and simplify.
Step 3.2.3.2.1
Divide each term in by .
Step 3.2.3.2.2
Simplify the left side.
Step 3.2.3.2.2.1
Cancel the common factor of .
Step 3.2.3.2.2.1.1
Cancel the common factor.
Step 3.2.3.2.2.1.2
Divide by .
Step 3.2.3.2.3
Simplify the right side.
Step 3.2.3.2.3.1
Cancel the common factor of and .
Step 3.2.3.2.3.1.1
Factor out of .
Step 3.2.3.2.3.1.2
Cancel the common factors.
Step 3.2.3.2.3.1.2.1
Factor out of .
Step 3.2.3.2.3.1.2.2
Cancel the common factor.
Step 3.2.3.2.3.1.2.3
Rewrite the expression.
Step 3.2.3.3
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 3.2.3.4
Simplify .
Step 3.2.3.4.1
Rewrite as .
Step 3.2.3.4.2
Simplify the numerator.
Step 3.2.3.4.2.1
Rewrite as .
Step 3.2.3.4.2.2
Pull terms out from under the radical, assuming positive real numbers.
Step 3.2.3.4.3
Multiply by .
Step 3.2.3.4.4
Combine and simplify the denominator.
Step 3.2.3.4.4.1
Multiply by .
Step 3.2.3.4.4.2
Raise to the power of .
Step 3.2.3.4.4.3
Raise to the power of .
Step 3.2.3.4.4.4
Use the power rule to combine exponents.
Step 3.2.3.4.4.5
Add and .
Step 3.2.3.4.4.6
Rewrite as .
Step 3.2.3.4.4.6.1
Use to rewrite as .
Step 3.2.3.4.4.6.2
Apply the power rule and multiply exponents, .
Step 3.2.3.4.4.6.3
Combine and .
Step 3.2.3.4.4.6.4
Cancel the common factor of .
Step 3.2.3.4.4.6.4.1
Cancel the common factor.
Step 3.2.3.4.4.6.4.2
Rewrite the expression.
Step 3.2.3.4.4.6.5
Evaluate the exponent.
Step 3.2.3.5
The complete solution is the result of both the positive and negative portions of the solution.
Step 3.2.3.5.1
First, use the positive value of the to find the first solution.
Step 3.2.3.5.2
Next, use the negative value of the to find the second solution.
Step 3.2.3.5.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 3.3
Replace all occurrences of with in each equation.
Step 3.3.1
Replace all occurrences of in with .
Step 3.3.2
Simplify .
Step 3.3.2.1
Simplify the left side.
Step 3.3.2.1.1
Remove parentheses.
Step 3.3.2.2
Simplify the right side.
Step 3.3.2.2.1
Simplify .
Step 3.3.2.2.1.1
Simplify the numerator.
Step 3.3.2.2.1.1.1
To write as a fraction with a common denominator, multiply by .
Step 3.3.2.2.1.1.2
Combine and .
Step 3.3.2.2.1.1.3
Combine the numerators over the common denominator.
Step 3.3.2.2.1.1.4
Multiply by .
Step 3.3.2.2.1.1.5
To write as a fraction with a common denominator, multiply by .
Step 3.3.2.2.1.1.6
Combine and .
Step 3.3.2.2.1.1.7
Combine the numerators over the common denominator.
Step 3.3.2.2.1.1.8
Multiply by .
Step 3.3.2.2.1.1.9
Multiply by .
Step 3.3.2.2.1.1.10
Simplify the numerator.
Step 3.3.2.2.1.1.10.1
Expand using the FOIL Method.
Step 3.3.2.2.1.1.10.1.1
Apply the distributive property.
Step 3.3.2.2.1.1.10.1.2
Apply the distributive property.
Step 3.3.2.2.1.1.10.1.3
Apply the distributive property.
Step 3.3.2.2.1.1.10.2
Simplify and combine like terms.
Step 3.3.2.2.1.1.10.2.1
Simplify each term.
Step 3.3.2.2.1.1.10.2.1.1
Multiply by .
Step 3.3.2.2.1.1.10.2.1.2
Multiply by .
Step 3.3.2.2.1.1.10.2.1.3
Multiply by .
Step 3.3.2.2.1.1.10.2.1.4
Multiply .
Step 3.3.2.2.1.1.10.2.1.4.1
Multiply by .
Step 3.3.2.2.1.1.10.2.1.4.2
Raise to the power of .
Step 3.3.2.2.1.1.10.2.1.4.3
Raise to the power of .
Step 3.3.2.2.1.1.10.2.1.4.4
Use the power rule to combine exponents.
Step 3.3.2.2.1.1.10.2.1.4.5
Add and .
Step 3.3.2.2.1.1.10.2.1.5
Rewrite as .
Step 3.3.2.2.1.1.10.2.1.5.1
Use to rewrite as .
Step 3.3.2.2.1.1.10.2.1.5.2
Apply the power rule and multiply exponents, .
Step 3.3.2.2.1.1.10.2.1.5.3
Combine and .
Step 3.3.2.2.1.1.10.2.1.5.4
Cancel the common factor of .
Step 3.3.2.2.1.1.10.2.1.5.4.1
Cancel the common factor.
Step 3.3.2.2.1.1.10.2.1.5.4.2
Rewrite the expression.
Step 3.3.2.2.1.1.10.2.1.5.5
Evaluate the exponent.
Step 3.3.2.2.1.1.10.2.1.6
Multiply by .
Step 3.3.2.2.1.1.10.2.2
Subtract from .
Step 3.3.2.2.1.1.10.2.3
Add and .
Step 3.3.2.2.1.1.10.2.4
Add and .
Step 3.3.2.2.1.1.11
Multiply by .
Step 3.3.2.2.1.1.12
Cancel the common factor of and .
Step 3.3.2.2.1.1.12.1
Factor out of .
Step 3.3.2.2.1.1.12.2
Cancel the common factors.
Step 3.3.2.2.1.1.12.2.1
Factor out of .
Step 3.3.2.2.1.1.12.2.2
Cancel the common factor.
Step 3.3.2.2.1.1.12.2.3
Rewrite the expression.
Step 3.3.2.2.1.1.13
Rewrite as .
Step 3.3.2.2.1.1.14
Simplify the numerator.
Step 3.3.2.2.1.1.14.1
Rewrite as .
Step 3.3.2.2.1.1.14.2
Pull terms out from under the radical, assuming positive real numbers.
Step 3.3.2.2.1.1.15
Multiply by .
Step 3.3.2.2.1.1.16
Combine and simplify the denominator.
Step 3.3.2.2.1.1.16.1
Multiply by .
Step 3.3.2.2.1.1.16.2
Raise to the power of .
Step 3.3.2.2.1.1.16.3
Raise to the power of .
Step 3.3.2.2.1.1.16.4
Use the power rule to combine exponents.
Step 3.3.2.2.1.1.16.5
Add and .
Step 3.3.2.2.1.1.16.6
Rewrite as .
Step 3.3.2.2.1.1.16.6.1
Use to rewrite as .
Step 3.3.2.2.1.1.16.6.2
Apply the power rule and multiply exponents, .
Step 3.3.2.2.1.1.16.6.3
Combine and .
Step 3.3.2.2.1.1.16.6.4
Cancel the common factor of .
Step 3.3.2.2.1.1.16.6.4.1
Cancel the common factor.
Step 3.3.2.2.1.1.16.6.4.2
Rewrite the expression.
Step 3.3.2.2.1.1.16.6.5
Evaluate the exponent.
Step 3.3.2.2.1.2
Combine and .
Step 3.3.2.2.1.3
Multiply by .
Step 3.3.2.2.1.4
Multiply the numerator by the reciprocal of the denominator.
Step 3.3.2.2.1.5
Cancel the common factor of .
Step 3.3.2.2.1.5.1
Factor out of .
Step 3.3.2.2.1.5.2
Cancel the common factor.
Step 3.3.2.2.1.5.3
Rewrite the expression.
Step 3.4
Replace all occurrences of with in each equation.
Step 3.4.1
Replace all occurrences of in with .
Step 3.4.2
Simplify .
Step 3.4.2.1
Simplify the left side.
Step 3.4.2.1.1
Remove parentheses.
Step 3.4.2.2
Simplify the right side.
Step 3.4.2.2.1
Simplify .
Step 3.4.2.2.1.1
Simplify the numerator.
Step 3.4.2.2.1.1.1
To write as a fraction with a common denominator, multiply by .
Step 3.4.2.2.1.1.2
Combine and .
Step 3.4.2.2.1.1.3
Combine the numerators over the common denominator.
Step 3.4.2.2.1.1.4
Multiply by .
Step 3.4.2.2.1.1.5
Multiply .
Step 3.4.2.2.1.1.5.1
Multiply by .
Step 3.4.2.2.1.1.5.2
Multiply by .
Step 3.4.2.2.1.1.6
To write as a fraction with a common denominator, multiply by .
Step 3.4.2.2.1.1.7
Combine and .
Step 3.4.2.2.1.1.8
Combine the numerators over the common denominator.
Step 3.4.2.2.1.1.9
Multiply by .
Step 3.4.2.2.1.1.10
Multiply by .
Step 3.4.2.2.1.1.11
Simplify the numerator.
Step 3.4.2.2.1.1.11.1
Expand using the FOIL Method.
Step 3.4.2.2.1.1.11.1.1
Apply the distributive property.
Step 3.4.2.2.1.1.11.1.2
Apply the distributive property.
Step 3.4.2.2.1.1.11.1.3
Apply the distributive property.
Step 3.4.2.2.1.1.11.2
Simplify and combine like terms.
Step 3.4.2.2.1.1.11.2.1
Simplify each term.
Step 3.4.2.2.1.1.11.2.1.1
Multiply by .
Step 3.4.2.2.1.1.11.2.1.2
Multiply by .
Step 3.4.2.2.1.1.11.2.1.3
Multiply by .
Step 3.4.2.2.1.1.11.2.1.4
Multiply .
Step 3.4.2.2.1.1.11.2.1.4.1
Multiply by .
Step 3.4.2.2.1.1.11.2.1.4.2
Raise to the power of .
Step 3.4.2.2.1.1.11.2.1.4.3
Raise to the power of .
Step 3.4.2.2.1.1.11.2.1.4.4
Use the power rule to combine exponents.
Step 3.4.2.2.1.1.11.2.1.4.5
Add and .
Step 3.4.2.2.1.1.11.2.1.5
Rewrite as .
Step 3.4.2.2.1.1.11.2.1.5.1
Use to rewrite as .
Step 3.4.2.2.1.1.11.2.1.5.2
Apply the power rule and multiply exponents, .
Step 3.4.2.2.1.1.11.2.1.5.3
Combine and .
Step 3.4.2.2.1.1.11.2.1.5.4
Cancel the common factor of .
Step 3.4.2.2.1.1.11.2.1.5.4.1
Cancel the common factor.
Step 3.4.2.2.1.1.11.2.1.5.4.2
Rewrite the expression.
Step 3.4.2.2.1.1.11.2.1.5.5
Evaluate the exponent.
Step 3.4.2.2.1.1.11.2.1.6
Multiply by .
Step 3.4.2.2.1.1.11.2.2
Subtract from .
Step 3.4.2.2.1.1.11.2.3
Subtract from .
Step 3.4.2.2.1.1.11.2.4
Add and .
Step 3.4.2.2.1.1.12
Multiply by .
Step 3.4.2.2.1.1.13
Cancel the common factor of and .
Step 3.4.2.2.1.1.13.1
Factor out of .
Step 3.4.2.2.1.1.13.2
Cancel the common factors.
Step 3.4.2.2.1.1.13.2.1
Factor out of .
Step 3.4.2.2.1.1.13.2.2
Cancel the common factor.
Step 3.4.2.2.1.1.13.2.3
Rewrite the expression.
Step 3.4.2.2.1.1.14
Rewrite as .
Step 3.4.2.2.1.1.15
Simplify the numerator.
Step 3.4.2.2.1.1.15.1
Rewrite as .
Step 3.4.2.2.1.1.15.2
Pull terms out from under the radical, assuming positive real numbers.
Step 3.4.2.2.1.1.16
Multiply by .
Step 3.4.2.2.1.1.17
Combine and simplify the denominator.
Step 3.4.2.2.1.1.17.1
Multiply by .
Step 3.4.2.2.1.1.17.2
Raise to the power of .
Step 3.4.2.2.1.1.17.3
Raise to the power of .
Step 3.4.2.2.1.1.17.4
Use the power rule to combine exponents.
Step 3.4.2.2.1.1.17.5
Add and .
Step 3.4.2.2.1.1.17.6
Rewrite as .
Step 3.4.2.2.1.1.17.6.1
Use to rewrite as .
Step 3.4.2.2.1.1.17.6.2
Apply the power rule and multiply exponents, .
Step 3.4.2.2.1.1.17.6.3
Combine and .
Step 3.4.2.2.1.1.17.6.4
Cancel the common factor of .
Step 3.4.2.2.1.1.17.6.4.1
Cancel the common factor.
Step 3.4.2.2.1.1.17.6.4.2
Rewrite the expression.
Step 3.4.2.2.1.1.17.6.5
Evaluate the exponent.
Step 3.4.2.2.1.2
Combine and .
Step 3.4.2.2.1.3
Multiply by .
Step 3.4.2.2.1.4
Multiply the numerator by the reciprocal of the denominator.
Step 3.4.2.2.1.5
Cancel the common factor of .
Step 3.4.2.2.1.5.1
Factor out of .
Step 3.4.2.2.1.5.2
Cancel the common factor.
Step 3.4.2.2.1.5.3
Rewrite the expression.
Step 4
The solution to the system is the complete set of ordered pairs that are valid solutions.
Step 5
The result can be shown in multiple forms.
Point Form:
Equation Form:
Step 6