Algebra Examples

Solve by Factoring x^(2/3)-2x^(1/3)-8=0
Step 1
Rewrite as .
Step 2
Let . Substitute for all occurrences of .
Step 3
Factor using the AC method.
Tap for more steps...
Step 3.1
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Step 3.2
Write the factored form using these integers.
Step 4
Replace all occurrences of with .
Step 5
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 6
Set equal to and solve for .
Tap for more steps...
Step 6.1
Set equal to .
Step 6.2
Solve for .
Tap for more steps...
Step 6.2.1
Add to both sides of the equation.
Step 6.2.2
Raise each side of the equation to the power of to eliminate the fractional exponent on the left side.
Step 6.2.3
Simplify the exponent.
Tap for more steps...
Step 6.2.3.1
Simplify the left side.
Tap for more steps...
Step 6.2.3.1.1
Simplify .
Tap for more steps...
Step 6.2.3.1.1.1
Multiply the exponents in .
Tap for more steps...
Step 6.2.3.1.1.1.1
Apply the power rule and multiply exponents, .
Step 6.2.3.1.1.1.2
Cancel the common factor of .
Tap for more steps...
Step 6.2.3.1.1.1.2.1
Cancel the common factor.
Step 6.2.3.1.1.1.2.2
Rewrite the expression.
Step 6.2.3.1.1.2
Simplify.
Step 6.2.3.2
Simplify the right side.
Tap for more steps...
Step 6.2.3.2.1
Raise to the power of .
Step 7
Set equal to and solve for .
Tap for more steps...
Step 7.1
Set equal to .
Step 7.2
Solve for .
Tap for more steps...
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.
Tap for more steps...
Step 7.2.3.1
Simplify the left side.
Tap for more steps...
Step 7.2.3.1.1
Simplify .
Tap for more steps...
Step 7.2.3.1.1.1
Multiply the exponents in .
Tap for more steps...
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 .
Tap for more steps...
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.
Tap for more steps...
Step 7.2.3.2.1
Raise to the power of .
Step 8
The final solution is all the values that make true.