Solve −2x2 − 16x − 44 = 0. x equals negative 8 plus or minus i square root of 6 x equals negative 8 plus or minus 2i square root of 6 x equals negative 4 plus or minus i square root of 6 x equals negative 4 plus or minus 2i square root of 6

I would immediately reduce this by div. every term by -2:

x^2 + 8x + 22 = 0

Next, I'd "complete the square:"

x^2 + 8x    + (4)^2  - (4)^2 + 22 = 0

   (x + 4)^2  - 16 + 22 = 0, so that (x+4)^2 + 4 = 0.

Then sqrt(   (x+4)^2  = sqrt(-4)

                     x+4      = plus or minus i*2

                      x          = -4 plus or minus i*2   (answer)