Divide each term in by .

Simplify each term.

Cancel the common factor of .

Cancel the common factor.

Divide by .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Divide by .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of .

Add the term to each side of the equation.

One to any power is one.

Simplify .

One to any power is one.

Write as a fraction with a common denominator.

Combine the numerators over the common denominator.

Add and .

Factor the perfect trinomial square into .

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 .

Simplify the right side of the equation.

Rewrite as .

Simplify the numerator.

Rewrite as .

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

Simplify the denominator.

Rewrite as .

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

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

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.

To write as a fraction with a common denominator, multiply by .

Combine and .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Subtract from .

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.

To write as a fraction with a common denominator, multiply by .

Combine and .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Subtract from .

Move the negative in front of the fraction.

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

Solve by Completing the Square 8x^2+16x=42