completing the square

Question

x^2+8x+12=0

Answer 1

x² + 8x + 12 = 0 Form is a² + bx + c = 0

Coefficient of x² is 1, so no division required. "b" term is 8, so b/2 = 8/2 = 4

Move the 12 to other side of equal sign: x² + 8x = -12 (Subtract 12 from both sides)

(b/2)² is 4². Add to both sides: x² + 8x + 4² = -12 + 16

Use the coefficients of the x² term and the 4² to create (x + 4)² = -12 + 16 = 4

Take the sq rt of both sides: x + 4 = ± 2

So the two solutions are: x + 4 = 2 -> x = -2 and x + 4 = -2 -> x = -6

You should always check by substituting back into the original equation.

Also - didn't really need to use complete the square method. The two factors of 12 that add to 8 are 6 and 2. Hence (x + 2)(x + 6) = 0, etc.