X2+8x+20=0 solve fo x over the compex numbers

You can use the quadratic formula but if you have to factor do the following:
x^2+8x+20=0
add -4 to both sides of the equation to complete the square
x^2+8x+20+(-4)=0+(-4)
x^2+8x+16=-4
(x+4)^2=-4
take the square root of both sides
x+4=+sqrt(-4)
x+4=+sqrt[(4)(-1)]
x+4=+2sqrt(-1) where sqrt(-1)=i, a complex number
x+4=+2i
x=-4+2i
x=-4+2i and x=-4-2i
you would get the same answer using the quadratic formula

Looks pretty good to me!