Question

Solve 2x2 + 8x - 12 = 0 by completing the square. What are the solutions

Answer 1

we gotta divide out the 2 then

and we are left with: x^2 +4x -6

to complete a square means this:

\begin{array}c
x^2&x&x\\
x&1&2\\
x&3&4
\end{array}
x^2 + 4x + 4 is a complete square; so add 4 and subtract 4 to our equaiton

Answer 2

factor out a 2
x^2 +4x -6 = 0
take half middle coefficient and square it
x^2 +4x +4 -6 = 4
(x+2)^2 = 10
x+2 = sqrt(10)
x = +-sqrt(10) -2

Answer 3

x^2 +4x +(4 -4) -6 = 0 ; regroup

(x^2 +4x +4) +(-4 -6) = 0 ; compact the square

(x+2)^2 -10 = 0

(x+2)^2 = 10 ; now this would be ideal if we had (sqrt(10))^2 but we have to subtract a 2 out if to make that work.

x = -2 +- sqrt(10)