1. Warm – up #7
1. Solve by Factoring 3 𝑥 2 −𝑥=2 2. Solve by Factoring 2 𝑥 2 =72 3. Solve 𝑥 2 =−5𝑥 4. Solve by Square Root (𝑥+3) 2 =−20

2. Warm – up #7 Solutions –6
1. Solve by Factoring 3 𝑥 2 −𝑥=2 3 𝑥 2 −𝑥−2=0 3 𝑥 2 −3𝑥+2𝑥−2=0 3x(x – 1) + 2(x – 1) = 0 (3x + 2)(x – 1) = 0 3x + 2 = 0 x – 1 = 0 x = 1, − 2 3 –3 2 –1

3. Warm – up #7 Solutions
2. Solve by factoring 2 𝑥 2 =72 2 𝑥 2 −72=0 2( 𝑥 2 −36)=0 = ( ) 2 − 2 = 2(x – 6)(x + 6) x – 6 = 0 x + 6 = 0 x = ±6 x 6

4. Warm – up #7 Solutions
3. Solve 𝑥 2 =−5𝑥 𝑥 2 +5𝑥=0 x(x + 5) = 0 x = 0, –5 4. Solve by Square Root (𝑥+3) 2 =−20 x + 3 = ±2𝑖 5 x=−3±2𝑖 5

5. Homework Log Thurs 11/12 Lesson 4 – 6 Learning Objective:
To solve quadratic equations by factoring
Hw: Lesson 4 – 6 WS

6. 11/12/15 Lesson 4 – 6 Completing the Square
Algebra II

7. Learning Objective
To solve quadratic equations by completing the square

8. Complete the Square 1. 𝑥 2 +2𝑥+_____ = (𝑥+1) 2 1 2. 𝑥 2 +4𝑥+_____
2. 𝑥 2 +4𝑥+_____
= (𝑥+2) 2 4

9. Complete the Square 3. 𝑥 2 +6𝑥+_____ = (𝑥+3) 2 9 4. 𝑥 2 +8𝑥+____
4. 𝑥 2 +8𝑥+____
= (𝑥+4) 2 16

10. Complete the Square 5. 𝑥 2 +10𝑥+_____ = (𝑥+5) 2 25 7. 𝑥 2 −20𝑥+_____
7. 𝑥 2 −20𝑥+_____
= (𝑥−10) 2
100
6. 𝑥 2 −2𝑥+____
= (𝑥−1) 2 1
8. 𝑥 2 −14𝑥+____
= (𝑥−7) 2 49

11. Complete the Square To Complete the Square 𝑥 2 +𝑏𝑥+_____
𝑥 2 MUST have a coefficient of 1
𝑏 goes in the blank
𝑏 2 goes into the perfect square (𝑥+ 𝑏 2 ) 2
𝑥 2 −12x+c

12. Solve by Square Root
9. (2𝑥+3) 2 = 4 2x + 3 = ±2 2x = – 3 ± 2 x = −3 ± 2 2 x = − x = −3 − 2 2
don’t forget!
−1 2 , −5 2

13. Solve by Completing the Square
10. 𝑥 2 −14𝑥+49 = 4
– 49 – 49
𝑥 2 −14𝑥 = – 45 +
− = (−7) 2 =49
(𝑥−7) 2 =4
x – 7 = ±2
x = 7±2
x = = 9
x = 7 – 2 = 5 49 49
5, 9

14. Solve by Completing the Square
11. 𝑥 2 +6𝑥 = –8
𝑥 2 +6𝑥 = – 8 +
= (3) 2 =9
(𝑥+3) 2 =1
x +3 = ±1
x = −3±1
x = – = –2
x = –3 – 1 = –4 9 9
−2, −4

15. Solve by Completing the Square
12. 𝑥 2 −8𝑥+28 = 4 – 28 – 28 𝑥 2 −8𝑥+ = – 24 + −8 2 2 = (−4) 2 =16 (𝑥−4) 2 =−8 x – 4 = ±2𝑖 2 16 16
4±2𝑖 2

16. Solve by Completing the Square
13. 𝑥 2 +6𝑥+13 = 0 – 13 – 13 𝑥 2 +6𝑥+ = – = (3) 2 =9 (𝑥+3) 2 =−4 x + 3 = ±2𝑖 9 9
−3±2𝑖

17. Solve by Completing the Square
14. 8𝑥 2 −16𝑥+104 = 8 – 104 – 104 8𝑥 2 −16𝑥 = – 𝑥 2 −2𝑥+ = –12 + −2 2 2 = (−1) 2 =1 (𝑥−1) 2 =−11 𝑥−1 = ±𝑖 11 1±𝑖 11 1 1

18. Solve by Completing the Square
Divide every term by leading coeff.
15. 2𝑥 2 −2𝑥+1 = 𝑥 2 −𝑥+ 1 2 = 0 – 1 2 – 1 2 𝑥 2 −𝑥+ = – −1 2 2 = 1 4
(𝑥− 1 2 ) 2 =− 1 4
𝑥− = ± 𝑖 2
1 2 ± 𝑖 2
or { 1±𝑖 2 }
1 4
1 4

19. Solve by Completing the Square
16. 𝑥 2 +3𝑥+12 = 0 – 12 – 12 𝑥 2 +3𝑥+ = – = 9 4 𝑥 =− 39 4
𝑥+ 3 2 = ±𝑖
− 3 2 ± 𝑖
or −3±𝑖
9 4
9 4

20. Ticket Out the Door 2𝑥 2 −20𝑥=−44 Solve by Completing the Square
Solve by Quadratic Formula
Do you get the same answer?

21. Assignment: Lesson 4 – 6 WS