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

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.
Multiply the exponents in .
Apply the power rule and multiply exponents, .
Cancel the common factor of .
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.
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.
Set the next factor equal to .
Find a common factor that is present in each term.
Substitute for .
Solve for .
Multiply by .
Use the quadratic formula to find the solutions.
Substitute the values , , and into the quadratic formula and solve for .
Simplify.
Simplify the numerator.
Raise to the power of .
Multiply by .
Multiply by .
Subtract from .
Rewrite as .
Rewrite as .
Rewrite as .
Rewrite as .
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 .
Simplify the numerator.
Raise to the power of .
Multiply by .
Multiply by .
Subtract from .
Rewrite as .
Rewrite as .
Rewrite as .
Rewrite as .
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 .
Simplify the numerator.
Raise to the power of .
Multiply by .
Multiply by .
Subtract from .
Rewrite as .
Rewrite as .
Rewrite as .
Rewrite as .
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 .
Raise each side of the equation to the power to eliminate the fractional exponent on the left side.
Simplify .
Use the power rule to distribute the exponent.
Apply the product rule to .
Apply the product rule to .
Simplify the expression.
Raise to the power of .
Multiply by .
Raise to the power of .
Rewrite as .
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Simplify each term.
Multiply by .
Multiply by .
Multiply by .
Multiply .
Multiply by .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite as .
Multiply by .
Rewrite as .
Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Evaluate the exponent.
Multiply by .
Subtract from .
Subtract from .
Reorder and .
Cancel the common factor of and .
Factor out of .
Factor out of .
Factor out of .
Cancel the common factors.
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 .
Raise each side of the equation to the power to eliminate the fractional exponent on the left side.
Simplify .
Use the power rule to distribute the exponent.
Apply the product rule to .
Apply the product rule to .
Simplify the expression.
Raise to the power of .
Multiply by .
Raise to the power of .
Rewrite as .
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Simplify each term.
Multiply by .
Multiply by .
Multiply by .
Multiply .
Multiply by .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite as .
Multiply by .
Rewrite as .
Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Evaluate the exponent.
Multiply by .
Subtract from .
Reorder and .
Cancel the common factor of and .
Factor out of .
Factor out of .
Factor out of .
Cancel the common factors.
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