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

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

3. 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.

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

5. Solve by completing the square.
STEPS
12) x2 + 12x + 35 = 0
x x = -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.
x x =
(x + 6)2 = 1
3) Divide the coefficient of the linear term – x – by 2, square the result, add to both sides.
x = ±1
x = -6 ± 1
x = = -5
x =-6 – 1 = -7
4) Solve.
{-7, -5}

6. 13) x2 – 4x = 12
ANSWER : {-2, 6}

7. 14) 4x2 + 8x + 1 = 0

8. 15) 2x2 – 20x = 40

9. 16) Solve using the Square Root Method.

10. COMPLETING THE SQUARE