# Precalculus Examples

,

Rewrite the equation as .

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Divide by .

Take the square root of each side of the equation to set up the solution for .

Remove the perfect root factor under the radical to solve for .

Rewrite as .

Pull terms out from under the radical, assuming positive real numbers.

First, use the positive value of the to find the first solution.

Move all terms not containing to the right side of the equation.

Subtract from both sides of the equation.

Subtract from .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Move the negative in front of the fraction.

Next, use the negative value of the to find the second solution.

Move all terms not containing to the right side of the equation.

Subtract from both sides of the equation.

Subtract from .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Move the negative in front of the fraction.

The complete solution is the result of both the positive and negative portions of the solution.

The interval does not contain . It is not part of the final solution.

is not on the interval

The interval contains .