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Algebra Examples
Step 1
Subtract from both sides of the equation.
Step 2
Use to rewrite as .
Step 3
Step 3.1
Factor out of .
Step 3.2
Factor out of .
Step 3.3
Factor out of .
Step 4
Rewrite as .
Step 5
Rewrite as .
Step 6
Since both terms are perfect cubes, factor using the difference of cubes formula, where and .
Step 7
Step 7.1
Simplify.
Step 7.1.1
Multiply the exponents in .
Step 7.1.1.1
Apply the power rule and multiply exponents, .
Step 7.1.1.2
Cancel the common factor of .
Step 7.1.1.2.1
Cancel the common factor.
Step 7.1.1.2.2
Rewrite the expression.
Step 7.1.2
Simplify.
Step 7.1.3
Multiply by .
Step 7.1.4
One to any power is one.
Step 7.2
Remove unnecessary parentheses.
Step 8
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 9
Step 9.1
Set equal to .
Step 9.2
Solve for .
Step 9.2.1
Raise each side of the equation to the power of to eliminate the fractional exponent on the left side.
Step 9.2.2
Simplify the exponent.
Step 9.2.2.1
Simplify the left side.
Step 9.2.2.1.1
Simplify .
Step 9.2.2.1.1.1
Multiply the exponents in .
Step 9.2.2.1.1.1.1
Apply the power rule and multiply exponents, .
Step 9.2.2.1.1.1.2
Cancel the common factor of .
Step 9.2.2.1.1.1.2.1
Cancel the common factor.
Step 9.2.2.1.1.1.2.2
Rewrite the expression.
Step 9.2.2.1.1.2
Simplify.
Step 9.2.2.2
Simplify the right side.
Step 9.2.2.2.1
Raising to any positive power yields .
Step 10
Step 10.1
Set equal to .
Step 10.2
Solve for .
Step 10.2.1
Add to both sides of the equation.
Step 10.2.2
Raise each side of the equation to the power of to eliminate the fractional exponent on the left side.
Step 10.2.3
Simplify the exponent.
Step 10.2.3.1
Simplify the left side.
Step 10.2.3.1.1
Simplify .
Step 10.2.3.1.1.1
Multiply the exponents in .
Step 10.2.3.1.1.1.1
Apply the power rule and multiply exponents, .
Step 10.2.3.1.1.1.2
Cancel the common factor of .
Step 10.2.3.1.1.1.2.1
Cancel the common factor.
Step 10.2.3.1.1.1.2.2
Rewrite the expression.
Step 10.2.3.1.1.2
Simplify.
Step 10.2.3.2
Simplify the right side.
Step 10.2.3.2.1
One to any power is one.
Step 11
Step 11.1
Set equal to .
Step 11.2
Solve for .
Step 11.2.1
Find a common factor that is present in each term.
Step 11.2.2
Substitute for .
Step 11.2.3
Solve for .
Step 11.2.3.1
Remove parentheses.
Step 11.2.3.2
Use the quadratic formula to find the solutions.
Step 11.2.3.3
Substitute the values , , and into the quadratic formula and solve for .
Step 11.2.3.4
Simplify.
Step 11.2.3.4.1
Simplify the numerator.
Step 11.2.3.4.1.1
One to any power is one.
Step 11.2.3.4.1.2
Multiply .
Step 11.2.3.4.1.2.1
Multiply by .
Step 11.2.3.4.1.2.2
Multiply by .
Step 11.2.3.4.1.3
Subtract from .
Step 11.2.3.4.1.4
Rewrite as .
Step 11.2.3.4.1.5
Rewrite as .
Step 11.2.3.4.1.6
Rewrite as .
Step 11.2.3.4.2
Multiply by .
Step 11.2.3.5
Simplify the expression to solve for the portion of the .
Step 11.2.3.5.1
Simplify the numerator.
Step 11.2.3.5.1.1
One to any power is one.
Step 11.2.3.5.1.2
Multiply .
Step 11.2.3.5.1.2.1
Multiply by .
Step 11.2.3.5.1.2.2
Multiply by .
Step 11.2.3.5.1.3
Subtract from .
Step 11.2.3.5.1.4
Rewrite as .
Step 11.2.3.5.1.5
Rewrite as .
Step 11.2.3.5.1.6
Rewrite as .
Step 11.2.3.5.2
Multiply by .
Step 11.2.3.5.3
Change the to .
Step 11.2.3.5.4
Rewrite as .
Step 11.2.3.5.5
Factor out of .
Step 11.2.3.5.6
Factor out of .
Step 11.2.3.5.7
Move the negative in front of the fraction.
Step 11.2.3.6
Simplify the expression to solve for the portion of the .
Step 11.2.3.6.1
Simplify the numerator.
Step 11.2.3.6.1.1
One to any power is one.
Step 11.2.3.6.1.2
Multiply .
Step 11.2.3.6.1.2.1
Multiply by .
Step 11.2.3.6.1.2.2
Multiply by .
Step 11.2.3.6.1.3
Subtract from .
Step 11.2.3.6.1.4
Rewrite as .
Step 11.2.3.6.1.5
Rewrite as .
Step 11.2.3.6.1.6
Rewrite as .
Step 11.2.3.6.2
Multiply by .
Step 11.2.3.6.3
Change the to .
Step 11.2.3.6.4
Rewrite as .
Step 11.2.3.6.5
Factor out of .
Step 11.2.3.6.6
Factor out of .
Step 11.2.3.6.7
Move the negative in front of the fraction.
Step 11.2.3.7
The final answer is the combination of both solutions.
Step 11.2.4
Substitute for .
Step 11.2.5
Solve for for .
Step 11.2.5.1
Raise each side of the equation to the power of to eliminate the fractional exponent on the left side.
Step 11.2.5.2
Simplify the exponent.
Step 11.2.5.2.1
Simplify the left side.
Step 11.2.5.2.1.1
Simplify .
Step 11.2.5.2.1.1.1
Multiply the exponents in .
Step 11.2.5.2.1.1.1.1
Apply the power rule and multiply exponents, .
Step 11.2.5.2.1.1.1.2
Cancel the common factor of .
Step 11.2.5.2.1.1.1.2.1
Cancel the common factor.
Step 11.2.5.2.1.1.1.2.2
Rewrite the expression.
Step 11.2.5.2.1.1.2
Simplify.
Step 11.2.5.2.2
Simplify the right side.
Step 11.2.5.2.2.1
Simplify .
Step 11.2.5.2.2.1.1
Use the power rule to distribute the exponent.
Step 11.2.5.2.2.1.1.1
Apply the product rule to .
Step 11.2.5.2.2.1.1.2
Apply the product rule to .
Step 11.2.5.2.2.1.2
Simplify the expression.
Step 11.2.5.2.2.1.2.1
Raise to the power of .
Step 11.2.5.2.2.1.2.2
Multiply by .
Step 11.2.5.2.2.1.2.3
Raise to the power of .
Step 11.2.5.2.2.1.2.4
Rewrite as .
Step 11.2.5.2.2.1.3
Expand using the FOIL Method.
Step 11.2.5.2.2.1.3.1
Apply the distributive property.
Step 11.2.5.2.2.1.3.2
Apply the distributive property.
Step 11.2.5.2.2.1.3.3
Apply the distributive property.
Step 11.2.5.2.2.1.4
Simplify and combine like terms.
Step 11.2.5.2.2.1.4.1
Simplify each term.
Step 11.2.5.2.2.1.4.1.1
Multiply by .
Step 11.2.5.2.2.1.4.1.2
Multiply by .
Step 11.2.5.2.2.1.4.1.3
Multiply by .
Step 11.2.5.2.2.1.4.1.4
Multiply .
Step 11.2.5.2.2.1.4.1.4.1
Multiply by .
Step 11.2.5.2.2.1.4.1.4.2
Multiply by .
Step 11.2.5.2.2.1.4.1.4.3
Raise to the power of .
Step 11.2.5.2.2.1.4.1.4.4
Raise to the power of .
Step 11.2.5.2.2.1.4.1.4.5
Use the power rule to combine exponents.
Step 11.2.5.2.2.1.4.1.4.6
Add and .
Step 11.2.5.2.2.1.4.1.4.7
Raise to the power of .
Step 11.2.5.2.2.1.4.1.4.8
Raise to the power of .
Step 11.2.5.2.2.1.4.1.4.9
Use the power rule to combine exponents.
Step 11.2.5.2.2.1.4.1.4.10
Add and .
Step 11.2.5.2.2.1.4.1.5
Rewrite as .
Step 11.2.5.2.2.1.4.1.5.1
Use to rewrite as .
Step 11.2.5.2.2.1.4.1.5.2
Apply the power rule and multiply exponents, .
Step 11.2.5.2.2.1.4.1.5.3
Combine and .
Step 11.2.5.2.2.1.4.1.5.4
Cancel the common factor of .
Step 11.2.5.2.2.1.4.1.5.4.1
Cancel the common factor.
Step 11.2.5.2.2.1.4.1.5.4.2
Rewrite the expression.
Step 11.2.5.2.2.1.4.1.5.5
Evaluate the exponent.
Step 11.2.5.2.2.1.4.1.6
Rewrite as .
Step 11.2.5.2.2.1.4.1.7
Multiply by .
Step 11.2.5.2.2.1.4.2
Subtract from .
Step 11.2.5.2.2.1.4.3
Subtract from .
Step 11.2.5.2.2.1.5
Reorder and .
Step 11.2.5.2.2.1.6
Cancel the common factor of and .
Step 11.2.5.2.2.1.6.1
Factor out of .
Step 11.2.5.2.2.1.6.2
Factor out of .
Step 11.2.5.2.2.1.6.3
Factor out of .
Step 11.2.5.2.2.1.6.4
Cancel the common factors.
Step 11.2.5.2.2.1.6.4.1
Factor out of .
Step 11.2.5.2.2.1.6.4.2
Cancel the common factor.
Step 11.2.5.2.2.1.6.4.3
Rewrite the expression.
Step 11.2.5.2.2.1.7
Rewrite as .
Step 11.2.5.2.2.1.8
Factor out of .
Step 11.2.5.2.2.1.9
Factor out of .
Step 11.2.5.2.2.1.10
Move the negative in front of the fraction.
Step 11.2.6
Solve for for .
Step 11.2.6.1
Raise each side of the equation to the power of to eliminate the fractional exponent on the left side.
Step 11.2.6.2
Simplify the exponent.
Step 11.2.6.2.1
Simplify the left side.
Step 11.2.6.2.1.1
Simplify .
Step 11.2.6.2.1.1.1
Multiply the exponents in .
Step 11.2.6.2.1.1.1.1
Apply the power rule and multiply exponents, .
Step 11.2.6.2.1.1.1.2
Cancel the common factor of .
Step 11.2.6.2.1.1.1.2.1
Cancel the common factor.
Step 11.2.6.2.1.1.1.2.2
Rewrite the expression.
Step 11.2.6.2.1.1.2
Simplify.
Step 11.2.6.2.2
Simplify the right side.
Step 11.2.6.2.2.1
Simplify .
Step 11.2.6.2.2.1.1
Use the power rule to distribute the exponent.
Step 11.2.6.2.2.1.1.1
Apply the product rule to .
Step 11.2.6.2.2.1.1.2
Apply the product rule to .
Step 11.2.6.2.2.1.2
Simplify the expression.
Step 11.2.6.2.2.1.2.1
Raise to the power of .
Step 11.2.6.2.2.1.2.2
Multiply by .
Step 11.2.6.2.2.1.2.3
Raise to the power of .
Step 11.2.6.2.2.1.2.4
Rewrite as .
Step 11.2.6.2.2.1.3
Expand using the FOIL Method.
Step 11.2.6.2.2.1.3.1
Apply the distributive property.
Step 11.2.6.2.2.1.3.2
Apply the distributive property.
Step 11.2.6.2.2.1.3.3
Apply the distributive property.
Step 11.2.6.2.2.1.4
Simplify and combine like terms.
Step 11.2.6.2.2.1.4.1
Simplify each term.
Step 11.2.6.2.2.1.4.1.1
Multiply by .
Step 11.2.6.2.2.1.4.1.2
Multiply by .
Step 11.2.6.2.2.1.4.1.3
Multiply by .
Step 11.2.6.2.2.1.4.1.4
Multiply .
Step 11.2.6.2.2.1.4.1.4.1
Raise to the power of .
Step 11.2.6.2.2.1.4.1.4.2
Raise to the power of .
Step 11.2.6.2.2.1.4.1.4.3
Use the power rule to combine exponents.
Step 11.2.6.2.2.1.4.1.4.4
Add and .
Step 11.2.6.2.2.1.4.1.4.5
Raise to the power of .
Step 11.2.6.2.2.1.4.1.4.6
Raise to the power of .
Step 11.2.6.2.2.1.4.1.4.7
Use the power rule to combine exponents.
Step 11.2.6.2.2.1.4.1.4.8
Add and .
Step 11.2.6.2.2.1.4.1.5
Rewrite as .
Step 11.2.6.2.2.1.4.1.6
Rewrite as .
Step 11.2.6.2.2.1.4.1.6.1
Use to rewrite as .
Step 11.2.6.2.2.1.4.1.6.2
Apply the power rule and multiply exponents, .
Step 11.2.6.2.2.1.4.1.6.3
Combine and .
Step 11.2.6.2.2.1.4.1.6.4
Cancel the common factor of .
Step 11.2.6.2.2.1.4.1.6.4.1
Cancel the common factor.
Step 11.2.6.2.2.1.4.1.6.4.2
Rewrite the expression.
Step 11.2.6.2.2.1.4.1.6.5
Evaluate the exponent.
Step 11.2.6.2.2.1.4.1.7
Multiply by .
Step 11.2.6.2.2.1.4.2
Subtract from .
Step 11.2.6.2.2.1.4.3
Add and .
Step 11.2.6.2.2.1.5
Reorder and .
Step 11.2.6.2.2.1.6
Cancel the common factor of and .
Step 11.2.6.2.2.1.6.1
Factor out of .
Step 11.2.6.2.2.1.6.2
Factor out of .
Step 11.2.6.2.2.1.6.3
Factor out of .
Step 11.2.6.2.2.1.6.4
Cancel the common factors.
Step 11.2.6.2.2.1.6.4.1
Factor out of .
Step 11.2.6.2.2.1.6.4.2
Cancel the common factor.
Step 11.2.6.2.2.1.6.4.3
Rewrite the expression.
Step 11.2.6.2.2.1.7
Rewrite as .
Step 11.2.6.2.2.1.8
Factor out of .
Step 11.2.6.2.2.1.9
Factor out of .
Step 11.2.6.2.2.1.10
Move the negative in front of the fraction.
Step 11.2.7
List all of the solutions.
Step 12
The final solution is all the values that make true.