1. Completing the Square

2. Why?
Why?
Why are we learning it?
Why?
Why?
Why?
Completing the Square allows us to solve unfactorable quadratic equations.

3. There will be two types of problems:
x2 + bx + c = 0
ax2 + bx + c = 0

4. Solving x2 + bx + c = 0 Process: Move the constant.
Determine what must be added to form a “perfect square”.
Factor.
Square root.
Solve what is left.

5. x2 + 6x + 2 = 0 -2 -2 x2 + 6x + = -2 Move the constant.
Putting it into action!
x2 + 6x + 2 = 0
x2 + 6x + = -2
Move the constant.
Subtract 2 from each side.
Leave a space where the 2 was, we’ll fill it in shortly.

6. x2 + 6x = -2
(3)
Determine what must be added to form a “perfect square”.
How to do it:
Take half of “b”. 6/2 = 3
Square this number. (3)2 = 9
Add to both sides.

7. x2 + 6x + (3)2 = -2 + 9 ( )2 = 7 x + 3 Factor.
( )2 = 7 x + 3
Factor.
The left side is now a perfect square trinomial.

8. (x + 3)2 = 7
x + 3 = 
Square root!!
Remember the “”

9.  x = -3 7  x + 3 = 7 -3 -3 Solve what is left.
x = 
Solve what is left.
Subtract 3 from both sides.

10. One more time: x2 + 6x + 2 = 0 x2 + 6x = -2 x2 + 6x + (3)2 = -2 + 9
Move the constant.
x2 + 6x = -2
Form a “perfect square”.
x2 + 6x + (3)2 =
Factor.
(x + 3)2 = 7
(x + 3)2 = 7
Square root.
x + 3 = ± 7
x = -3 ± 7
Solve what is left.

11. Solving ax2 + bx + c = 0 Process: Divide each term by “a”.
Move the constant.
Form a “perfect square”.
Factor.
Square root.
Solve what is left.

12. 2x2 + 8x - 3 = 0 2 2 2 2 x2 + 4x - = 0 3 2 Divide each term by “a”.
Doing it!
2x2 + 8x - 3 = 0
x2 + 4x - = 0 3 2
Divide each term by “a”.
Divide each term by 2.
Don’t use decimals.

13. x2 + 4x - = 0 + + x2 + 4x + = 3 2 3 2 3 2 Move the constant.
+ +
x2 + 4x + = 3 2
Move the constant.
Add 3/2 to each side.
Leave a space where the -3/2 was, we’ll fill it in shortly.

14. x2 + 4x = 3 2
(2)
Determine what must be added to form a “perfect square”.
How to do it:
Take half of “b”. 4/2 = 2
Square this number. (2)2 = 4
Add to both sides.

15. x2 + 4x + (2)2= 3 2
( )2 = 11 2 x + 2
Factor.
The left side is now a perfect square trinomial.

16. (x + 2)2 = 11 2
x + 2 =  11 2
Square root!!
Remember the “”

17. x = -2  x + 2 =  -2 -2 x = -2  11 2 11 2 22 2 Solve what is left.
x = -2 11 2 
x = -2  22 2
Solve what is left.
Subtract 2 from both sides.
Rationalize the denominator.

18. Solving ax2 + bx + c = 0 Process: Divide each term by “a”.
Move the constant.
Form a “perfect square”.
Factor.
Square root.
Solve what is left.

19. 
The End!!!                