K(H) = - ( x^2 + 1)^2 + 4 ....so
-(x^2 + 1)^2 + 4 = 0
-(x^2 + 1)^2 = -4 multiply through by -1
(x^2 + 1)^2 = 4 take the pos/neg square roots
x^2 + 1 = ± 2
So...either
x^2 + 1 = 2 subtract 1 from both sides
x^2 = 1 take both square roots
x = ± 1
Or
x^2 + 1 = -2 subtract 1 from both sides
x^2 = -3 take both square roots
x = ± (√3) i
And those are the 4 solutions