COMPLETING THE SQUARE - ANSWERS

 

1. x2 -8x -2 = 0

x2 -8x -2 = 0
(x - 4)2 - 18 = 0
(x - 4)2 = 18
x - 4 = ± Ö18
x = 4 ± Ö18

Note we always put + or - in front of the square root sign because the square roots of a positive number can be either positive or negative. For example: Ö4 = 2 or -2 (as 2 x 2 = 4 and -2 x -2 = 4)
2. x2 + 10x + 3 = 0
x2 + 10x + 3 = 0
(x + 5)2 - 22 = 0
x = -5 ± Ö22

3. x2 -6x + 2 = 0 x2 -6x + 2 = 0
(x - 3)2 - 7 = 0
x = 3 ± Ö7

4. x2 -4x - 3 = 0 x2 -4x - 3 = 0
(x - 2)2 - 7 = 0
x = 2 ± Ö7
5. x2 + 10x + 18 = 0

x2 + 10x + 18 = 0
(x + 5)2 - 7 = 0
x = -5 ± Ö7

6. 2x2 + 8x + 2 = 0 2x2 + 8x + 2 = 0
2(x2 + 4x + 1) = 0
(x + 2)2 - 3 = 0
x = -2 ± Ö3
7. 3x2 -6x + 1 = 0 3x2 -6x + 1 = 0
3(x2 -2x + 1/3) = 0
(x - 1)2 - 2/3 = 0
x = 1 ± Ö2/3
8. 4y2 - y = 8

      4y2 - y - 8 = 0
4(y2 - 1/4y - 2) = 0
     y2 - 1/4y - 2 = 0
(y - 1/8)2 - 33/16   = 0
(y - 1/8)2 = 33/16
y - 1/8 = ± Ö33/16
x = 1/8 ± Ö33/16