Question

How do you solve `z^2 +12 = -z`?

Answer 1

`-1/2±sqrt(47)/2i`

Explanation:

Use the quadratic formula

`z^2+12=-z <=> z^2+z+12=0`

`z=(-1±sqrt(1^2-4(12)(1)))/2=-1/2±sqrt(47)/2i`

Alternatively, you could complete the square,

`z^2+z+12=0`
`z^2+z+1/4 + 47/4 =0`
`(z+1/2)^2=-47/4`
`z+1/2=+-sqrt(47)/2i`
`z=-1/2+-sqrt(47)/2i`

Which yields the same result (the quadratic formula is derived from completing the square)