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Calculus Examples
Step 1
Subtract from both sides of the equation.
Step 2
To remove the radical on the left side of the equation, square both sides of the equation.
Step 3
Step 3.1
Use to rewrite as .
Step 3.2
Simplify the left side.
Step 3.2.1
Simplify .
Step 3.2.1.1
Multiply the exponents in .
Step 3.2.1.1.1
Apply the power rule and multiply exponents, .
Step 3.2.1.1.2
Cancel the common factor of .
Step 3.2.1.1.2.1
Cancel the common factor.
Step 3.2.1.1.2.2
Rewrite the expression.
Step 3.2.1.2
Simplify.
Step 3.3
Simplify the right side.
Step 3.3.1
Simplify .
Step 3.3.1.1
Rewrite as .
Step 3.3.1.2
Expand using the FOIL Method.
Step 3.3.1.2.1
Apply the distributive property.
Step 3.3.1.2.2
Apply the distributive property.
Step 3.3.1.2.3
Apply the distributive property.
Step 3.3.1.3
Simplify and combine like terms.
Step 3.3.1.3.1
Simplify each term.
Step 3.3.1.3.1.1
Multiply by .
Step 3.3.1.3.1.2
Multiply by .
Step 3.3.1.3.1.3
Multiply by .
Step 3.3.1.3.1.4
Multiply .
Step 3.3.1.3.1.4.1
Multiply by .
Step 3.3.1.3.1.4.2
Multiply by .
Step 3.3.1.3.1.4.3
Raise to the power of .
Step 3.3.1.3.1.4.4
Raise to the power of .
Step 3.3.1.3.1.4.5
Use the power rule to combine exponents.
Step 3.3.1.3.1.4.6
Add and .
Step 3.3.1.3.1.5
Rewrite as .
Step 3.3.1.3.1.5.1
Use to rewrite as .
Step 3.3.1.3.1.5.2
Apply the power rule and multiply exponents, .
Step 3.3.1.3.1.5.3
Combine and .
Step 3.3.1.3.1.5.4
Cancel the common factor of .
Step 3.3.1.3.1.5.4.1
Cancel the common factor.
Step 3.3.1.3.1.5.4.2
Rewrite the expression.
Step 3.3.1.3.1.5.5
Simplify.
Step 3.3.1.3.2
Add and .
Step 3.3.1.3.3
Subtract from .
Step 4
Step 4.1
Rewrite the equation as .
Step 4.2
Move all terms not containing to the right side of the equation.
Step 4.2.1
Subtract from both sides of the equation.
Step 4.2.2
Subtract from both sides of the equation.
Step 4.2.3
Subtract from .
Step 4.2.4
Subtract from .
Step 5
To remove the radical on the left side of the equation, square both sides of the equation.
Step 6
Step 6.1
Use to rewrite as .
Step 6.2
Simplify the left side.
Step 6.2.1
Simplify .
Step 6.2.1.1
Apply the product rule to .
Step 6.2.1.2
Raise to the power of .
Step 6.2.1.3
Multiply the exponents in .
Step 6.2.1.3.1
Apply the power rule and multiply exponents, .
Step 6.2.1.3.2
Cancel the common factor of .
Step 6.2.1.3.2.1
Cancel the common factor.
Step 6.2.1.3.2.2
Rewrite the expression.
Step 6.2.1.4
Simplify.
Step 6.2.1.5
Apply the distributive property.
Step 6.2.1.6
Multiply by .
Step 6.3
Simplify the right side.
Step 6.3.1
Simplify .
Step 6.3.1.1
Rewrite as .
Step 6.3.1.2
Expand using the FOIL Method.
Step 6.3.1.2.1
Apply the distributive property.
Step 6.3.1.2.2
Apply the distributive property.
Step 6.3.1.2.3
Apply the distributive property.
Step 6.3.1.3
Simplify and combine like terms.
Step 6.3.1.3.1
Simplify each term.
Step 6.3.1.3.1.1
Rewrite using the commutative property of multiplication.
Step 6.3.1.3.1.2
Multiply by by adding the exponents.
Step 6.3.1.3.1.2.1
Move .
Step 6.3.1.3.1.2.2
Multiply by .
Step 6.3.1.3.1.3
Multiply by .
Step 6.3.1.3.1.4
Multiply by .
Step 6.3.1.3.1.5
Multiply by .
Step 6.3.1.3.1.6
Multiply by .
Step 6.3.1.3.2
Subtract from .
Step 7
Step 7.1
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 7.2
Move all terms containing to the left side of the equation.
Step 7.2.1
Subtract from both sides of the equation.
Step 7.2.2
Subtract from .
Step 7.3
Subtract from both sides of the equation.
Step 7.4
Subtract from .
Step 7.5
Factor out of .
Step 7.5.1
Factor out of .
Step 7.5.2
Factor out of .
Step 7.5.3
Factor out of .
Step 7.5.4
Factor out of .
Step 7.5.5
Factor out of .
Step 7.6
Divide each term in by and simplify.
Step 7.6.1
Divide each term in by .
Step 7.6.2
Simplify the left side.
Step 7.6.2.1
Cancel the common factor of .
Step 7.6.2.1.1
Cancel the common factor.
Step 7.6.2.1.2
Divide by .
Step 7.6.3
Simplify the right side.
Step 7.6.3.1
Divide by .
Step 7.7
Use the quadratic formula to find the solutions.
Step 7.8
Substitute the values , , and into the quadratic formula and solve for .
Step 7.9
Simplify.
Step 7.9.1
Simplify the numerator.
Step 7.9.1.1
Raise to the power of .
Step 7.9.1.2
Multiply .
Step 7.9.1.2.1
Multiply by .
Step 7.9.1.2.2
Multiply by .
Step 7.9.1.3
Subtract from .
Step 7.9.2
Multiply by .
Step 7.10
The final answer is the combination of both solutions.
Step 8
Exclude the solutions that do not make true.