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Algebra Examples
Step 1
Rewrite as .
Step 2
Rewrite as .
Step 3
Since both terms are perfect cubes, factor using the difference of cubes formula, where and .
Step 4
Step 4.1
Rewrite as .
Step 4.2
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 4.3
Multiply by .
Step 5
Step 5.1
Multiply the exponents in .
Step 5.1.1
Apply the power rule and multiply exponents, .
Step 5.1.2
Multiply by .
Step 5.2
One to any power is one.
Step 6
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 7
Step 7.1
Set equal to .
Step 7.2
Subtract from both sides of the equation.
Step 8
Step 8.1
Set equal to .
Step 8.2
Add to both sides of the equation.
Step 9
Step 9.1
Set equal to .
Step 9.2
Solve for .
Step 9.2.1
Substitute into the equation. This will make the quadratic formula easy to use.
Step 9.2.2
Use the quadratic formula to find the solutions.
Step 9.2.3
Substitute the values , , and into the quadratic formula and solve for .
Step 9.2.4
Simplify.
Step 9.2.4.1
Simplify the numerator.
Step 9.2.4.1.1
One to any power is one.
Step 9.2.4.1.2
Multiply .
Step 9.2.4.1.2.1
Multiply by .
Step 9.2.4.1.2.2
Multiply by .
Step 9.2.4.1.3
Subtract from .
Step 9.2.4.1.4
Rewrite as .
Step 9.2.4.1.5
Rewrite as .
Step 9.2.4.1.6
Rewrite as .
Step 9.2.4.2
Multiply by .
Step 9.2.5
Simplify the expression to solve for the portion of the .
Step 9.2.5.1
Simplify the numerator.
Step 9.2.5.1.1
One to any power is one.
Step 9.2.5.1.2
Multiply .
Step 9.2.5.1.2.1
Multiply by .
Step 9.2.5.1.2.2
Multiply by .
Step 9.2.5.1.3
Subtract from .
Step 9.2.5.1.4
Rewrite as .
Step 9.2.5.1.5
Rewrite as .
Step 9.2.5.1.6
Rewrite as .
Step 9.2.5.2
Multiply by .
Step 9.2.5.3
Change the to .
Step 9.2.5.4
Rewrite as .
Step 9.2.5.5
Factor out of .
Step 9.2.5.6
Factor out of .
Step 9.2.5.7
Move the negative in front of the fraction.
Step 9.2.6
Simplify the expression to solve for the portion of the .
Step 9.2.6.1
Simplify the numerator.
Step 9.2.6.1.1
One to any power is one.
Step 9.2.6.1.2
Multiply .
Step 9.2.6.1.2.1
Multiply by .
Step 9.2.6.1.2.2
Multiply by .
Step 9.2.6.1.3
Subtract from .
Step 9.2.6.1.4
Rewrite as .
Step 9.2.6.1.5
Rewrite as .
Step 9.2.6.1.6
Rewrite as .
Step 9.2.6.2
Multiply by .
Step 9.2.6.3
Change the to .
Step 9.2.6.4
Rewrite as .
Step 9.2.6.5
Factor out of .
Step 9.2.6.6
Factor out of .
Step 9.2.6.7
Move the negative in front of the fraction.
Step 9.2.7
The final answer is the combination of both solutions.
Step 9.2.8
Substitute the real value of back into the solved equation.
Step 9.2.9
Solve the first equation for .
Step 9.2.10
Solve the equation for .
Step 9.2.10.1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 9.2.10.2
Simplify .
Step 9.2.10.2.1
Rewrite as .
Step 9.2.10.2.1.1
Rewrite as .
Step 9.2.10.2.1.2
Rewrite as .
Step 9.2.10.2.2
Pull terms out from under the radical.
Step 9.2.10.2.3
One to any power is one.
Step 9.2.10.2.4
Rewrite as .
Step 9.2.10.2.5
Multiply by .
Step 9.2.10.2.6
Combine and simplify the denominator.
Step 9.2.10.2.6.1
Multiply by .
Step 9.2.10.2.6.2
Raise to the power of .
Step 9.2.10.2.6.3
Raise to the power of .
Step 9.2.10.2.6.4
Use the power rule to combine exponents.
Step 9.2.10.2.6.5
Add and .
Step 9.2.10.2.6.6
Rewrite as .
Step 9.2.10.2.6.6.1
Use to rewrite as .
Step 9.2.10.2.6.6.2
Apply the power rule and multiply exponents, .
Step 9.2.10.2.6.6.3
Combine and .
Step 9.2.10.2.6.6.4
Cancel the common factor of .
Step 9.2.10.2.6.6.4.1
Cancel the common factor.
Step 9.2.10.2.6.6.4.2
Rewrite the expression.
Step 9.2.10.2.6.6.5
Evaluate the exponent.
Step 9.2.10.2.7
Combine using the product rule for radicals.
Step 9.2.10.2.8
Combine and .
Step 9.2.10.2.9
Move to the left of .
Step 9.2.10.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 9.2.10.3.1
First, use the positive value of the to find the first solution.
Step 9.2.10.3.2
Next, use the negative value of the to find the second solution.
Step 9.2.10.3.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 9.2.11
Solve the second equation for .
Step 9.2.12
Solve the equation for .
Step 9.2.12.1
Remove parentheses.
Step 9.2.12.2
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 9.2.12.3
Simplify .
Step 9.2.12.3.1
Rewrite as .
Step 9.2.12.3.1.1
Rewrite as .
Step 9.2.12.3.1.2
Rewrite as .
Step 9.2.12.3.2
Pull terms out from under the radical.
Step 9.2.12.3.3
One to any power is one.
Step 9.2.12.3.4
Rewrite as .
Step 9.2.12.3.5
Multiply by .
Step 9.2.12.3.6
Combine and simplify the denominator.
Step 9.2.12.3.6.1
Multiply by .
Step 9.2.12.3.6.2
Raise to the power of .
Step 9.2.12.3.6.3
Raise to the power of .
Step 9.2.12.3.6.4
Use the power rule to combine exponents.
Step 9.2.12.3.6.5
Add and .
Step 9.2.12.3.6.6
Rewrite as .
Step 9.2.12.3.6.6.1
Use to rewrite as .
Step 9.2.12.3.6.6.2
Apply the power rule and multiply exponents, .
Step 9.2.12.3.6.6.3
Combine and .
Step 9.2.12.3.6.6.4
Cancel the common factor of .
Step 9.2.12.3.6.6.4.1
Cancel the common factor.
Step 9.2.12.3.6.6.4.2
Rewrite the expression.
Step 9.2.12.3.6.6.5
Evaluate the exponent.
Step 9.2.12.3.7
Combine using the product rule for radicals.
Step 9.2.12.3.8
Combine and .
Step 9.2.12.3.9
Move to the left of .
Step 9.2.12.4
The complete solution is the result of both the positive and negative portions of the solution.
Step 9.2.12.4.1
First, use the positive value of the to find the first solution.
Step 9.2.12.4.2
Next, use the negative value of the to find the second solution.
Step 9.2.12.4.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 9.2.13
The solution to is .
Step 10
The final solution is all the values that make true.