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

1 Answer
May 22, 2018

-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)