Solve by Factoring x^(3/2)=27

Math
Move to the left side of the equation by subtracting it from both sides.
Rewrite as .
Rewrite as .
Since both terms are perfect cubes, factor using the difference of cubes formula, where and .
Simplify.
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Multiply the exponents in .
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Apply the power rule and multiply exponents, .
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Simplify.
Move to the left of .
Raise to the power of .
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set the first factor equal to and solve.
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Set the first factor equal to .
Add to both sides of the equation.
Raise each side of the equation to the power to eliminate the fractional exponent on the left side.
Raise to the power of .
Set the next factor equal to and solve.
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Set the next factor equal to .
Find a common factor that is present in each term.
Substitute for .
Solve for .
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Multiply by .
Use the quadratic formula to find the solutions.
Substitute the values , , and into the quadratic formula and solve for .
Simplify.
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Simplify the numerator.
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Raise to the power of .
Multiply by .
Multiply by .
Subtract from .
Rewrite as .
Rewrite as .
Rewrite as .
Rewrite as .
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Factor out of .
Rewrite as .
Pull terms out from under the radical.
Move to the left of .
Multiply by .
Simplify the expression to solve for the portion of the .
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Simplify the numerator.
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Raise to the power of .
Multiply by .
Multiply by .
Subtract from .
Rewrite as .
Rewrite as .
Rewrite as .
Rewrite as .
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Factor out of .
Rewrite as .
Pull terms out from under the radical.
Move to the left of .
Multiply by .
Change the to .
Rewrite as .
Factor out of .
Factor out of .
Move the negative in front of the fraction.
Simplify the expression to solve for the portion of the .
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Simplify the numerator.
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Raise to the power of .
Multiply by .
Multiply by .
Subtract from .
Rewrite as .
Rewrite as .
Rewrite as .
Rewrite as .
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Factor out of .
Rewrite as .
Pull terms out from under the radical.
Move to the left of .
Multiply by .
Change the to .
Rewrite as .
Factor out of .
Factor out of .
Move the negative in front of the fraction.
The final answer is the combination of both solutions.
Substitute for .
Solve for for .
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Raise each side of the equation to the power to eliminate the fractional exponent on the left side.
Simplify .
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Use the power rule to distribute the exponent.
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Apply the product rule to .
Apply the product rule to .
Simplify the expression.
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Raise to the power of .
Multiply by .
Raise to the power of .
Rewrite as .
Expand using the FOIL Method.
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Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
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Simplify each term.
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Multiply by .
Multiply by .
Multiply by .
Multiply .
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Multiply by .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Rewrite as .
Multiply by .
Rewrite as .
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Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Evaluate the exponent.
Multiply by .
Subtract from .
Subtract from .
Reorder and .
Cancel the common factor of and .
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Factor out of .
Factor out of .
Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Rewrite as .
Factor out of .
Factor out of .
Move the negative in front of the fraction.
Solve for for .
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Raise each side of the equation to the power to eliminate the fractional exponent on the left side.
Simplify .
Tap for more steps…
Use the power rule to distribute the exponent.
Tap for more steps…
Apply the product rule to .
Apply the product rule to .
Simplify the expression.
Tap for more steps…
Raise to the power of .
Multiply by .
Raise to the power of .
Rewrite as .
Expand using the FOIL Method.
Tap for more steps…
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Tap for more steps…
Simplify each term.
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Multiply by .
Multiply by .
Multiply by .
Multiply .
Tap for more steps…
Multiply by .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Rewrite as .
Multiply by .
Rewrite as .
Tap for more steps…
Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Tap for more steps…
Cancel the common factor.
Divide by .
Evaluate the exponent.
Multiply by .
Subtract from .
Add and .
Reorder and .
Cancel the common factor of and .
Tap for more steps…
Factor out of .
Factor out of .
Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Rewrite as .
Factor out of .
Factor out of .
Move the negative in front of the fraction.
List all of the solutions.
The final solution is all the values that make true.
Solve by Factoring x^(3/2)=27

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