1. 9.4 – Solving Quadratic Equations By Completing The Square

2. Ex. 1 a. Solve x2 – 12x + 36 = 0.

3. Ex. 1 a. Solve x2 – 12x + 36 = 0.
x2 – 12x + 36 = 0

4. Ex. 1 a. Solve x2 – 12x + 36 = 0.
x2 – 12x + 36 = 0
(x )(x ) = 0

5. Ex. 1 a. Solve x2 – 12x + 36 = 0.
x2 – 12x + 36 = 0
(x – 6)(x – 6) = 0

6. Ex. 1 a. Solve x2 – 12x + 36 = 0.
x2 – 12x + 36 = 0
(x – 6)(x – 6) = 0
(x – 6)2 = 0

7. Ex. 1 a. Solve x2 – 12x + 36 = 0.
x2 – 12x + 36 = 0
(x – 6)(x – 6) = 0
√(x – 6)2 = √0

8. Ex. 1 a. Solve x2 – 12x + 36 = 0.
x2 – 12x + 36 = 0
(x – 6)(x – 6) = 0
√(x – 6)2 = √0
x – 6 = 0

9. Ex. 1 a. Solve x2 – 12x + 36 = 0.
x2 – 12x + 36 = 0
(x – 6)(x – 6) = 0
√(x – 6)2 = √0
x – 6 = 0
x = 6

10. b. Solve x2 + 8x + 16 = 0.

11. b. Solve x2 + 8x + 16 = 0.
x2 + 8x + 16 = 0
(x + 4)(x + 4) = 0
√(x + 4)2 = √ 0
x + 4 = 0
x = -4

12. b. Solve x2 + 8x + 16 = 0.
x2 + 8x + 16 = 0
(x + 4)(x + 4) = 0
(x + 4)2 = 0
x + 4 = 0
x = -4
Ex. 2 a. Solve x2 + 10x + 21 = 0 by completing the square.

13. b. Solve x2 + 8x + 16 = 0.
x2 + 8x + 16 = 0
(x + 4)(x + 4) = 0
(x + 4)2 = 0
x + 4 = 0
x = -4
Ex. 2 a. Solve x2 + 10x + 21 = 0 by completing the square.
x2 + 10x + 21 = 0

14. b. Solve x2 + 8x + 16 = 0.
x2 + 8x + 16 = 0
(x + 4)(x + 4) = 0
(x + 4)2 = 0
x + 4 = 0
x = -4
Ex. 2 a. Solve x2 + 10x + 21 = 0 by completing the square.
x2 + 10x + 21 = 0
Want x2 + 10x + 25

15. b. Solve x2 + 8x + 16 = 0.
x2 + 8x + 16 = 0
(x + 4)(x + 4) = 0
(x + 4)2 = 0
x + 4 = 0
x = -4
Ex. 2 a. Solve x2 + 10x + 21 = 0 by completing the square.
x2 + 10x + 21 = 0
x2 + 10x + 25 = 4

16. b. Solve x2 + 8x + 16 = 0.
x2 + 8x + 16 = 0
(x + 4)(x + 4) = 0
(x + 4)2 = 0
x + 4 = 0
x = -4
Ex. 2 a. Solve x2 + 10x + 21 = 0 by completing the square.
x2 + 10x + 21 = 0
x2 + 10x + 25 = 4
(x + 5)2 = 4

17. b. Solve x2 + 8x + 16 = 0.
x2 + 8x + 16 = 0
(x + 4)(x + 4) = 0
(x + 4)2 = 0
x + 4 = 0
x = -4
Ex. 2 a. Solve x2 + 10x + 21 = 0 by completing the square.
x2 + 10x + 21 = 0
x2 + 10x + 25 = 4
(x + 5)2 = 4
x + 5 = ±2

18. b. Solve x2 + 8x + 16 = 0.
x2 + 8x + 16 = 0
(x + 4)(x + 4) = 0
(x + 4)2 = 0
x + 4 = 0
x = -4
Ex. 2 a. Solve x2 + 10x + 21 = 0 by completing the square.
x2 + 10x + 21 = 0
x2 + 10x + 25 = 4
(x + 5)2 = 4
x + 5 = ±2
x + 5 = 2

19. b. Solve x2 + 8x + 16 = 0.
x2 + 8x + 16 = 0
(x + 4)(x + 4) = 0
(x + 4)2 = 0
x + 4 = 0
x = -4
Ex. 2 a. Solve x2 + 10x + 21 = 0 by completing the square.
x2 + 10x + 21 = 0
x2 + 10x + 25 = 4
(x + 5)2 = 4
x + 5 = ±2
x + 5 = 2 x + 5 = -2

20. b. Solve x2 + 8x + 16 = 0.
x2 + 8x + 16 = 0
(x + 4)(x + 4) = 0
(x + 4)2 = 0
x + 4 = 0
x = -4
Ex. 2 a. Solve x2 + 10x + 21 = 0 by completing the square.
x2 + 10x + 21 = 0
x2 + 10x + 25 = 4
(x + 5)2 = 4
x + 5 = ±2
x + 5 = 2 x + 5 = -2
x = -3

21. b. Solve x2 + 8x + 16 = 0.
x2 + 8x + 16 = 0
(x + 4)(x + 4) = 0
(x + 4)2 = 0
x + 4 = 0
x = -4
Ex. 2 a. Solve x2 + 10x + 21 = 0 by completing the square.
x2 + 10x + 21 = 0
x2 + 10x + 25 = 4
(x + 5)2 = 4
x + 5 = ±2
x + 5 = 2 x + 5 = -2
x = x = -7

22. b. Solve x2 + 14x = 12 by completing the square.

23. b. Solve x2 + 14x = 12 by completing the square.
Want x2 + 14x + 49
x2 + 14x + 49 = 61
(x + 7)2 = 61
x + 7 = ±√61
x = -7 ± √61
x ≈ 0.8 or x ≈ -14.8