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.

Simplify each term.

Apply the product rule to .

Raise to the power of .

Raise to the power of .

Simplify .

Simplify each term.

Apply the product rule to .

Raise to the power of .

Raise to the power of .

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 .

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.

Combine the numerators over the common denominator.

Subtract from .

Divide by .

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.

Combine the numerators over the common denominator.

Subtract from .

Divide by .

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

Solve by Completing the Square g^2+7g=144