Pre-Algebra Examples

Solve for x (8x^3-9)^3=5832
Step 1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 2
Simplify .
Tap for more steps...
Step 2.1
Rewrite as .
Step 2.2
Pull terms out from under the radical, assuming real numbers.
Step 3
Move all terms not containing to the right side of the equation.
Tap for more steps...
Step 3.1
Add to both sides of the equation.
Step 3.2
Add and .
Step 4
Subtract from both sides of the equation.
Step 5
Factor the left side of the equation.
Tap for more steps...
Step 5.1
Rewrite as .
Step 5.2
Rewrite as .
Step 5.3
Since both terms are perfect cubes, factor using the difference of cubes formula, where and .
Step 5.4
Simplify.
Tap for more steps...
Step 5.4.1
Apply the product rule to .
Step 5.4.2
Raise to the power of .
Step 5.4.3
Multiply by .
Step 5.4.4
Raise to the power of .
Step 6
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
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
Add to both sides of the equation.
Step 7.2.2
Divide each term in by and simplify.
Tap for more steps...
Step 7.2.2.1
Divide each term in by .
Step 7.2.2.2
Simplify the left side.
Tap for more steps...
Step 7.2.2.2.1
Cancel the common factor of .
Tap for more steps...
Step 7.2.2.2.1.1
Cancel the common factor.
Step 7.2.2.2.1.2
Divide by .
Step 8
Set equal to and solve for .
Tap for more steps...
Step 8.1
Set equal to .
Step 8.2
Solve for .
Tap for more steps...
Step 8.2.1
Use the quadratic formula to find the solutions.
Step 8.2.2
Substitute the values , , and into the quadratic formula and solve for .
Step 8.2.3
Simplify.
Tap for more steps...
Step 8.2.3.1
Simplify the numerator.
Tap for more steps...
Step 8.2.3.1.1
Raise to the power of .
Step 8.2.3.1.2
Multiply .
Tap for more steps...
Step 8.2.3.1.2.1
Multiply by .
Step 8.2.3.1.2.2
Multiply by .
Step 8.2.3.1.3
Subtract from .
Step 8.2.3.1.4
Rewrite as .
Step 8.2.3.1.5
Rewrite as .
Step 8.2.3.1.6
Rewrite as .
Step 8.2.3.1.7
Rewrite as .
Tap for more steps...
Step 8.2.3.1.7.1
Factor out of .
Step 8.2.3.1.7.2
Rewrite as .
Step 8.2.3.1.8
Pull terms out from under the radical.
Step 8.2.3.1.9
Move to the left of .
Step 8.2.3.2
Multiply by .
Step 8.2.3.3
Simplify .
Step 8.2.4
The final answer is the combination of both solutions.
Step 9
The final solution is all the values that make true.