1. ALGEBRA II HONORS @ COMPLETING THE SQUARE

2. Solve by factoring. 1) x 2 + 12x + 35 = 0 Get one side equal to 0. Factor.(x + 5)(x + 7) = 0 Set each factor equal to 0 and solve. x + 5 =0 x + 7 = 0 x = -5 x = -7 {-7, -5} 2) 3x 2 = x + 14

3. FOIL!! 3) (x + 4) 2 = (x + 4)(x + 4)  chin & grin 4) (y – 6) 2 ANSWER : y 2 – 12y + 36 5) (x – 8) 2 ANSWER : x 2 – 16x + 64 6) When you FOIL a square, what happens to the middle term? ANSWER : It doubles. = x 2 + 4x + 16 = x 2 + 8x + 16

4. Complete the Square. Think… 7) y 2 + 14y + ______ 8) x 2 – 6x + ______ 9) x 2 – x + _____ 10) x 2 + 3x + ______ ANSWER : 49 ANSWER : 9

5. Solve by completing the square. 12) x 2 + 12x + 35 = 0 STEPS 1) Variables on one side, constant on the other. x 2 + 12x = -35 2) Get the coefficient of the quadratic term – x 2 – to be 1. 3) Divide the coefficient of the linear term – x – by 2, square the result, add to both sides. 4) Solve. (6) 2 = 36 x 2 + 12x + 36 = -35 + 36 (x + 6) 2 = 1 x + 6 = ±1 x = -6 ± 1 x = -6 + 1 = -5x =-6 – 1 = -7 {-7, -5}

6. 13) x 2 – 4x = 12ANSWER : {-2, 6}

7. 14) 4x 2 + 8x + 1 = 0

8. 15) 2n 2 = n + 3

9. 16) 2x 2 – 20x = 40