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

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

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

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

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

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

Learning Objective To solve quadratic equations by completing the square

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

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

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

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

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

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

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

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

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

Solve by Completing the Square 14. 8𝑥 2 −16𝑥+104 = 8 – 104 – 104 8𝑥 2 −16𝑥 = –96 8 8 8 𝑥 2 −2𝑥+ = –12 + −2 2 2 = (−1) 2 =1 (𝑥−1) 2 =−11 𝑥−1 = ±𝑖 11 1±𝑖 11 1 1

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

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

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

Assignment: Lesson 4 – 6 WS