# Algebra Examples

Step 1

Add to both sides of the equation.

Step 2

Subtract from both sides of the equation.

Step 3

Step 3.1

Rewrite as .

Step 3.2

Since both terms are perfect cubes, factor using the difference of cubes formula, where and .

Step 3.3

Simplify.

Step 3.3.1

Move to the left of .

Step 3.3.2

Raise to the power of .

Step 4

If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .

Step 5

Step 5.1

Set equal to .

Step 5.2

Add to both sides of the equation.

Step 6

Step 6.1

Set equal to .

Step 6.2

Solve for .

Step 6.2.1

Use the quadratic formula to find the solutions.

Step 6.2.2

Substitute the values , , and into the quadratic formula and solve for .

Step 6.2.3

Simplify.

Step 6.2.3.1

Simplify the numerator.

Step 6.2.3.1.1

Raise to the power of .

Step 6.2.3.1.2

Multiply .

Step 6.2.3.1.2.1

Multiply by .

Step 6.2.3.1.2.2

Multiply by .

Step 6.2.3.1.3

Subtract from .

Step 6.2.3.1.4

Rewrite as .

Step 6.2.3.1.5

Rewrite as .

Step 6.2.3.1.6

Rewrite as .

Step 6.2.3.1.7

Rewrite as .

Step 6.2.3.1.7.1

Factor out of .

Step 6.2.3.1.7.2

Rewrite as .

Step 6.2.3.1.8

Pull terms out from under the radical.

Step 6.2.3.1.9

Move to the left of .

Step 6.2.3.2

Multiply by .

Step 6.2.3.3

Simplify .

Step 6.2.4

Simplify the expression to solve for the portion of the .

Step 6.2.4.1

Simplify the numerator.

Step 6.2.4.1.1

Raise to the power of .

Step 6.2.4.1.2

Multiply .

Step 6.2.4.1.2.1

Multiply by .

Step 6.2.4.1.2.2

Multiply by .

Step 6.2.4.1.3

Subtract from .

Step 6.2.4.1.4

Rewrite as .

Step 6.2.4.1.5

Rewrite as .

Step 6.2.4.1.6

Rewrite as .

Step 6.2.4.1.7

Rewrite as .

Step 6.2.4.1.7.1

Factor out of .

Step 6.2.4.1.7.2

Rewrite as .

Step 6.2.4.1.8

Pull terms out from under the radical.

Step 6.2.4.1.9

Move to the left of .

Step 6.2.4.2

Multiply by .

Step 6.2.4.3

Simplify .

Step 6.2.4.4

Change the to .

Step 6.2.5

Simplify the expression to solve for the portion of the .

Step 6.2.5.1

Simplify the numerator.

Step 6.2.5.1.1

Raise to the power of .

Step 6.2.5.1.2

Multiply .

Step 6.2.5.1.2.1

Multiply by .

Step 6.2.5.1.2.2

Multiply by .

Step 6.2.5.1.3

Subtract from .

Step 6.2.5.1.4

Rewrite as .

Step 6.2.5.1.5

Rewrite as .

Step 6.2.5.1.6

Rewrite as .

Step 6.2.5.1.7

Rewrite as .

Step 6.2.5.1.7.1

Factor out of .

Step 6.2.5.1.7.2

Rewrite as .

Step 6.2.5.1.8

Pull terms out from under the radical.

Step 6.2.5.1.9

Move to the left of .

Step 6.2.5.2

Multiply by .

Step 6.2.5.3

Simplify .

Step 6.2.5.4

Change the to .

Step 6.2.6

The final answer is the combination of both solutions.

Step 7

The final solution is all the values that make true.