1. Ch 10: Polynomials G) Completing the Square Objective: To solve quadratic equations by completing the square.

2. Methods for Solving Quadratic Equations 1) Square Root Method (Works when no “x” term) 2) Graphic Method (Works when on lattice point) x=-1x=3 3) Quadratic Formula a=1 b= -2 c= -3 (Always works) 4) Factoring Method (Works when factorable) 5) Completing the Square (Always works) * * x = ±3 x = −1, x = 3

3. Rules 1)Subtract c from both sides….. 2)Divide both sides by a……… 3)Divide the x term by 2............ 4)Add b 2 to both sides…….. (the left side is a “perfect square”) 5) Square root both sides……….. 6) Solve for x …………………... ax 2 + bx + c = 0from Standard Form: ax 2 + bx = −c x 2 + b x = −c a a x + b 2a 2 = −c + b 2 2a + b 2 2a + b 2 2a x 2 + b x = −c 2a x + b 2a 2 −c + b 2 2a √√ = a a a a 2 a | x + b/(2a)| = a

4. 6262 ( ) (x ) 2 = 7+ 3 2 = 9 + 9 Example 1 + 9 What number (c) makes this a Perfect Square?

5. Complete the perfect square trinomial -8 2 (x ) 2 = -5- 4 ( ) 2 = 16 + 16 Example 2

6. Complete the square Example 3

7. Complete the square Example 4

8. Classwork 1) 3) 2) 4) Find the value of c that completes the square y 2 − 14y + c x 2 + 12x + c r 2 + 26r + c2t 2 – 7t + c c = 49 c = 36 c = 169 c = 49 16 2 2 2 2 2 2 2 2 2 22

9. 5) 7) 6) 8) Solve each equation by completing the square x 2 – 4x – 34 = -2 x 2 − 12x – 60 = 4 n 2 + 8n – 26 = 72p 2 – 20p + 16 = -2 {-4, 8} {-4, 16} {-11, 3} {1, 9}