Question

Rewrite the equation by completing the square.
x² + 8x + 12 =10

Answer 1

(x+4)² - 14 =0

Explanation:

x² + 8x + 12 =10

(x²+4²) - 4²+12 = 10

(x+4)² -4-10 = 0

(x+4)² - 14 =0

Note: When completing squares, in the equation above.

• We square the half of 8.
• We add the result to x² , and subtract it with 12.

Answer 2

(x +4)^2 = 14

Explanation:

The constant on the left wants to be the square of half the coefficient of the linear term:

(8/2)^2 = 16

In order for it to be that value, we need to add 4 to the equation.

x^2 +8x +12 +4 = 10 +4

x^2 +8x +16 = 14 . . . . collect terms

(x +4)^2 = 14 . . . . . . . write as a square