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.

• One of the benefits to completing the square is that 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” coefficient3) Square the result in step 24) Add the result to both sides of the equation (this guarantees the equation stays balanced)5) Factor the left side; simplify the right side6) 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)