Question

Solve x2 + 4x – 12 = 0 by completing the square. Show your work for full credit.

Answer 1

first ask yourself what two numbers that are added or subtracted can give you the sum or difference of 4 and when multiplied give you a product of 12

Answer 2

To solve this by completing the square:

1. Put the constant (in this case, -12) on the other side:
x^2 + 4x = 12

2. Take the coefficient of the x-term (in this case, 4), HALVE it, then SQUARE it:
4/2 = 2
2^2 = 4

3. Add that to BOTH sides:
x^2 + 4x + 4 = 12 + 4 = 16

4. Simplify:
x^2 + 4x + 4 = 16
(x + 2)^2 = 16

5. Take the square root of both sides, and put in a ± on the right side:
(x+2)^2 = 16
x + 2 = ± 4

6. Simplify:
x = -2 ± 4

7. Evaluate:
x = -2 - 4 = -6
x = -2 + 4 = 2