ALGEBRA II HONORS/GIFTED - SECTION 4-6 (Completing the Square) @ SECTION 4-7 : COMPLETE THE SQUARE

Solve by factoring. 1) x2 + 12x + 35 = 0 Get one side equal to 0. (x + 5)(x + 7) = 0 Factor. x + 5 =0 x + 7 = 0 Set each factor equal to 0 and solve. x = -5 x = -7 {-7, -5} 2) 3x2 = x + 14

FOIL!! 3) (x + 4)2 = (x + 4)(x + 4) chin & grin = x2 + 4x + 4x + 16 = x2 + 8x + 16 4) (y – 6)2 ANSWER : y2 – 12y + 36 5) (x – 8)2 ANSWER : x2 – 16x + 64 6) When you FOIL a square, what happens to the middle term? ANSWER : It doubles.

Complete the Square. Think… 7) y2 + 14y + ______ ANSWER : 49 8) x2 – 6x + ______ ANSWER : 9 9) x2 – x + _____ 10) x2 + 3x + ______

Solve by completing the square. STEPS 12) x2 + 12x + 35 = 0 x2 + 12x = -35 1) Variables on one side, constant on the other. (6)2 = 36 2) Get the coefficient of the quadratic term – x2 – to be 1. x2 + 12x + 36 = -35 + 36 (x + 6)2 = 1 3) Divide the coefficient of the linear term – x – by 2, square the result, add to both sides. x + 6 = ±1 x = -6 ± 1 x = -6 + 1 = -5 x =-6 – 1 = -7 4) Solve. {-7, -5}

13) x2 – 4x = 12 ANSWER : {-2, 6}

14) 4x2 + 8x + 1 = 0

15) 2x2 – 20x = 40

16) Solve using the Square Root Method.

COMPLETING THE SQUARE