Finite Math Examples

Solve by Factoring cube root of (x+2)^2=16
Step 1
Subtract from both sides of the equation.
Step 2
Use to rewrite as .
Step 3
Rewrite as .
Step 4
Rewrite as .
Step 5
Since both terms are perfect squares, factor using the difference of squares formula, where and .
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
Set equal to and solve for .
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Step 7.1
Set equal to .
Step 7.2
Solve for .
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Step 7.2.1
Subtract from both sides of the equation.
Step 7.2.2
Raise each side of the equation to the power of to eliminate the fractional exponent on the left side.
Step 7.2.3
Simplify the exponent.
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Step 7.2.3.1
Simplify the left side.
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Step 7.2.3.1.1
Simplify .
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Step 7.2.3.1.1.1
Multiply the exponents in .
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Step 7.2.3.1.1.1.1
Apply the power rule and multiply exponents, .
Step 7.2.3.1.1.1.2
Cancel the common factor of .
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Step 7.2.3.1.1.1.2.1
Cancel the common factor.
Step 7.2.3.1.1.1.2.2
Rewrite the expression.
Step 7.2.3.1.1.2
Simplify.
Step 7.2.3.2
Simplify the right side.
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Step 7.2.3.2.1
Raise to the power of .
Step 7.2.4
Move all terms not containing to the right side of the equation.
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Step 7.2.4.1
Subtract from both sides of the equation.
Step 7.2.4.2
Subtract from .
Step 8
Set equal to and solve for .
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Step 8.1
Set equal to .
Step 8.2
Solve for .
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Step 8.2.1
Add to both sides of the equation.
Step 8.2.2
Raise each side of the equation to the power of to eliminate the fractional exponent on the left side.
Step 8.2.3
Simplify the exponent.
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Step 8.2.3.1
Simplify the left side.
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Step 8.2.3.1.1
Simplify .
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Step 8.2.3.1.1.1
Multiply the exponents in .
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Step 8.2.3.1.1.1.1
Apply the power rule and multiply exponents, .
Step 8.2.3.1.1.1.2
Cancel the common factor of .
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Step 8.2.3.1.1.1.2.1
Cancel the common factor.
Step 8.2.3.1.1.1.2.2
Rewrite the expression.
Step 8.2.3.1.1.2
Simplify.
Step 8.2.3.2
Simplify the right side.
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Step 8.2.3.2.1
Raise to the power of .
Step 8.2.4
Move all terms not containing to the right side of the equation.
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Step 8.2.4.1
Subtract from both sides of the equation.
Step 8.2.4.2
Subtract from .
Step 9
The final solution is all the values that make true.