Remove the absolute value term. This creates a on the right side of the equation because .

Set up the positive portion of the solution.

Move to the left side of the equation by subtracting it from both sides.

Factor using the AC method.

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 .

Write the factored form using these integers.

Set equal to and solve for .

Set the factor equal to .

Add to both sides of the equation.

Set equal to and solve for .

Set the factor equal to .

Subtract from both sides of the equation.

The solution is the result of and .

Set up the negative portion of the solution.

Move to the left side of the equation by adding it to both sides.

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 final answer is the combination of both solutions.

The solution to the equation includes both the positive and negative portions of the solution.

Solve for x |x^2-2x|=24