solve x : x^4 -4x^2 -32 = 0

x^4-4x^2-32 = 0 To solve for
x.

Solution:

This is a
quadratic equation in x^2. So we solve it  by factoring as a
quadratic.

t^2-4t-32 = 0, where t=
x^2

t^2-8t+4t-32 =
0

t(t-8)+4(t-8) = 0

(t-8)(t+4)
= 0

t-8 = 0 or t+4 = 0

t-8= 0
gives x^2 = 8 , x = +or- sqrt8 = 2sqrt2 or -2sqrt2

t+4 = 0
gives x = sqrt(-4) = +or-2i

So the solution set is {
-2i,2i, -2srt2, 2srt2}