Finite Math Examples

Solve for m cube root of m=m
Step 1
To remove the radical on the left side of the equation, cube both sides of the equation.
Step 2
Simplify each side of the equation.
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Step 2.1
Use to rewrite as .
Step 2.2
Simplify the left side.
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Step 2.2.1
Simplify .
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Step 2.2.1.1
Multiply the exponents in .
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Step 2.2.1.1.1
Apply the power rule and multiply exponents, .
Step 2.2.1.1.2
Cancel the common factor of .
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Step 2.2.1.1.2.1
Cancel the common factor.
Step 2.2.1.1.2.2
Rewrite the expression.
Step 2.2.1.2
Simplify.
Step 3
Solve for .
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Step 3.1
Subtract from both sides of the equation.
Step 3.2
Factor the left side of the equation.
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Step 3.2.1
Factor out of .
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Step 3.2.1.1
Raise to the power of .
Step 3.2.1.2
Factor out of .
Step 3.2.1.3
Factor out of .
Step 3.2.1.4
Factor out of .
Step 3.2.2
Rewrite as .
Step 3.2.3
Factor.
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Step 3.2.3.1
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 3.2.3.2
Remove unnecessary parentheses.
Step 3.3
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 3.4
Set equal to .
Step 3.5
Set equal to and solve for .
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Step 3.5.1
Set equal to .
Step 3.5.2
Subtract from both sides of the equation.
Step 3.6
Set equal to and solve for .
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Step 3.6.1
Set equal to .
Step 3.6.2
Solve for .
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Step 3.6.2.1
Subtract from both sides of the equation.
Step 3.6.2.2
Divide each term in by and simplify.
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Step 3.6.2.2.1
Divide each term in by .
Step 3.6.2.2.2
Simplify the left side.
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Step 3.6.2.2.2.1
Dividing two negative values results in a positive value.
Step 3.6.2.2.2.2
Divide by .
Step 3.6.2.2.3
Simplify the right side.
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Step 3.6.2.2.3.1
Divide by .
Step 3.7
The final solution is all the values that make true.