Completing the Square

Completing the Square

How do I complete the square?

Example:

 $x^2+40x+?$  

• How to find the last term...

• Divide the middle term by 2. ( $40\div2=20$ )

• Take the result and square it. ( $20^2=400$ )

• So, the answer is  $x^2+40x+400$  

• Remember the last term can NEVER be NEGATIVE because it is SQUARED.

Let's Practice!

Multiple Choice

Find the last term:

 $x^2+22x+c$  

• 22

• 11

• 121

• 44

Multiple Choice

Find the last term:

 $x^2-8x+c$  

• 8

• 4

• -16

• 16

Multiple Choice

Find the last term:

 $x^2-16x+c$  

• 8

• 64

• -16

• 16

Multiple Choice

Find the last term:

 $x^2+34x+c$  

• 289

• 17

• 34

• -34

Multiple Choice

Find the last term:

 $x^2+30x+c$  

• 30

• 15

• 225

• -15

Multiple Choice

Find the last term:

 $x^2+4x+c$  

• 4

• 2

• -2

• -4

Multiple Choice

Find the last term:

 $x^2-6x+c$  

• -9

• 9

• 6

• -6

Multiple Choice

Find the last term:

 $x^2+10x+c$  

• 5

• 2

• 20

• 25

Multiple Choice

Find the last term:

 $x^2+12x+c$  

• 36

• 21

• 16

• 25

Multiple Choice

Find the last term:

 $x^2+42x+c$  

• -9

• 21

• 441

• 1764

Multiple Choice

Find the last term:

 $x^2-2x+c$  

• -2

• 1

• -1

• 2

Multiple Choice

Find the last term:

 $x^2-28x+c$  

• 14

• 200

• 169

• 196