Completing the Square to Solve Quadratic Equations

The objective of the Completing the Square Method is to make one side of the equation a perfect square trinomial so that, when factored, we can take the square root of each side and solve.

The most involved part of the method is making the perfect square trinomial. Please read through each of the fol lowing examples before solving the equations on the worksheet.

Example: when and b is even:

Solve:

	1. Move the constant to the other side of the equation.
	2. Take half of the coefficient of x and square it.
	3. Add the number to both sides of the equation.
	4. Factor the trinomial on the left side of the equation and add the numbers on the right side of the equation.
	5. Take the square root of each side. Don’t forget the ± signs .
	6. Simplify the radicals .
	7. Solve for x.

Example: when and b is odd:

Solve:

	1. Move the constant to the other side of the equation.
	2. Take half of the coefficient of x and square it. (Leave the number as a fraction .)
	3. Add the number to both sides of the equation.
	4. Multiply each side of the equation by the LCD to remove the fraction . (LCD=4)
	5. Factor the trinomial on the left side of the equation and add the numbers on the right side of the equation.
	6. Take the square root of each side. Don’t forget the ± signs.
	7. Simplify the radicals.
	8. Set up two equations and solve each for x.