1. COMPLETING THE SQUARE

2. Remember when we learned:
Algebraic Identities?
(x + 2)2 = x2 + 4x + 4
and
(x – 2)2 = x2 – 4x + 4

3. Remember the SQUARE ROOT PROPERTY?
For any real number n,
if x2 = n, then x = + n
For example:
x2 = 16 therefore
x = + 4
x2 = 5 therefore
x = + 5

4. Remember: PERFECT SQUARE TRINOMIALS?
x2 + 8x + 16
The first term must be a perfect square…
x2 = ( x )( x )

5. Remember: PERFECT SQUARE TRINOMIALS?
x2 + 8x + 16
The third term must be a perfect square…
16 = ( 4 )( 4 )

6. Remember: PERFECT SQUARE TRINOMIALS?
x2 + 8x + 16
The middle term must
equal the sum of the
factors of the third term.
4 + 4 = 8

7. Remember: PERFECT SQUARE TRINOMIALS?
Now factor
x2 + 8x + 16 =
( x + 4 )( x +4 ) or ( x +4)2

8. Remember: PERFECT SQUARE TRINOMIALS?
x x
( x )( x ) + 2x + 2x + (2)(2)
Add the middle term.
Perfect squares

9. OKAY…ARE WE READY TO SOLVE Quadratic Equations by
Completing the Square?

10. Completing the Square Problem: y = x2 + 10x 0 = x2 + 10x 25
Step 1: Set y = 0
0 = x2 + 10x
What value do we need for “c” to make this a Perfect Square Trinomial? 25
0 = x2 + 10x
+ 25

11. Determine the c value that will complete these squares.1. 2. 3. 4. 5.
To determine “c”, divide “b” by 2 and then square the result.

12. Use Completing the Square to Solve this Quadratic Equation+1 +1
continued

13. or

14. Use Completing the Square to Solve this Quadratic Equation when “b” is not even!
continued

15. or

16. Use Completing the Square to Solve this Quadratic Equation when “a” is not one!
continued

17. or

18. Now It’s YOUR TURN !!!!

19. Solve:
3x2 + 12x = 5

20. And the answer is