Basic Math Examples

Solve for r -1/27=r^3
Step 1
Rewrite the equation as .
Step 2
Add to both sides of the equation.
Step 3
Factor the left side of the equation.
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Step 3.1
Rewrite as .
Step 3.2
Rewrite as .
Step 3.3
Rewrite as .
Step 3.4
Since both terms are perfect cubes, factor using the sum of cubes formula, where and .
Step 3.5
Simplify.
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Step 3.5.1
Combine and .
Step 3.5.2
Apply the product rule to .
Step 3.5.3
One to any power is one.
Step 3.5.4
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
Set equal to and solve for .
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Step 5.1
Set equal to .
Step 5.2
Subtract from both sides of the equation.
Step 6
Set equal to and solve for .
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Step 6.1
Set equal to .
Step 6.2
Solve for .
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Step 6.2.1
Multiply through by the least common denominator , then simplify.
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Step 6.2.1.1
Apply the distributive property.
Step 6.2.1.2
Simplify.
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Step 6.2.1.2.1
Cancel the common factor of .
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Step 6.2.1.2.1.1
Move the leading negative in into the numerator.
Step 6.2.1.2.1.2
Factor out of .
Step 6.2.1.2.1.3
Cancel the common factor.
Step 6.2.1.2.1.4
Rewrite the expression.
Step 6.2.1.2.2
Multiply by .
Step 6.2.1.2.3
Cancel the common factor of .
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Step 6.2.1.2.3.1
Cancel the common factor.
Step 6.2.1.2.3.2
Rewrite the expression.
Step 6.2.2
Use the quadratic formula to find the solutions.
Step 6.2.3
Substitute the values , , and into the quadratic formula and solve for .
Step 6.2.4
Simplify.
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Step 6.2.4.1
Simplify the numerator.
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Step 6.2.4.1.1
Raise to the power of .
Step 6.2.4.1.2
Multiply .
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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 .
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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 6.2.5
The final answer is the combination of both solutions.
Step 7
The final solution is all the values that make true.