Algebra I

What is completing the square used for?
►
Completing the square is used for all those not factorable problems!!
►
It is used to solve these equations for the variable.

Rule for Completing the Square x
2  bx x
2  bx
 b
2


 b

2
  x b
2 b
2


 2
2
This is now a PST!
So, it factors into this!

►
Example 1: Find the term that should be added to the expression to create a perfect square trinomial. X 2 - 3x + c

►
Example 2: Solve by completing the square.
X 2 -8x+12=0

►
Example 3: Solve by completing the square. 4x 2 - 8x = 24

Example 1: Find the term that should be added to the expression to create a perfect square trinomial.
X 2 - 3x + c
► b=-3 c
 b
2
2

2
3
2

9
4

Example 2: Solve by completing the square. X 2 -8x+12=0
► x 2 -8x+12=0 x 2 -8x=-12 x 2 -8x+___=-12+___
 b
2
2

2
8
2

 
2 
16
Don’t forget: Whatever you add to one side of an equation, you MUST add to the other side!
x 2 -8x+ 16=-12+16
(x-4)(x-4) = 4
(x-4) 2 =4 x

4
 
2 x

6 , 2

Example 3: Solve by completing the square. x 2 +6x-8=0
► x 2 +6x-8=0 x 2 +6x=8 x 2 +6x+___=8+___
 b
2
2

6
2
 2

  x 2 +6x+9=8+9
2 
9
(x+3) 2 =17
Don’t forget: Whatever you add to one side of an equation, you MUST add to the other side!
x

3
 
17 x
 
3

17