Completing the Square

Completing the Square

-forces any quadratic expression to factor

-use “completing the square” to solve quadratic equations

To Complete the Square:

Ex. x^2+6x+16=0

Note: a=1, b=6, c=-16

Step 1. Move the constant term ( c ) to one side and every other term to the other side.

x^2+6x-16=0 → x^2+6x=16

Step 2: Factor out the leading coefficient (a)

*will be more relevant when a does not equal 1.

1(x^2+6x)=16

Step 3: Add (1/2 x b)^2 to side with (a) and (b) term. Then add a(1/2 x b)^2 to the side with constant term.

Simplify:

1(x^2+6x+(6/2)^2)= 16+1(6/2)^2

x^2+6x+9=16+9

x^2+6x+9=25

Step 4: Factor side with (a) and (b) terms

(x+3)(x+3)=25 → (x+3)^2=25

*At this point you can either solve for x