6-4 Completing the Square Objective: Students will be able to solve quadratic equations by completing the square.

Another way to solve quadratic equations is by a method called completing the square. Benefit: you can still attain exact roots, even when a quadratic equation is not factorable. Let’s look at the steps for completing the square…

Steps for completing the square: 1)Set your equation to the form: (the “a” coefficient on the x must be 1) 2) Find half of your “b” coefficient 3) Square the result in step 2 4) Add the result to both sides of the equation (this guarantees the equation stays balanced) 5) Factor the left side; simplify the right side 6) Solve the equation

Let’s solve the same equation two ways: first by factoring, and then by completing the square. Factoring

Completing the square

Solve each equation by completing the square. 1)

2)

3)

4)

Try these. 5) 6)

Application (from text p. 310) The area A in square feet of a projected picture on a movie screen is given by A = 0.16d 2, where d is the distance from the projector to the screen in feet. At what distance will the projected picture have an area of 100 square feet?

Homework Text p. 311 #s even