Solve for x:
x^4+x^2-2 = 0
Substitute y = x^2:
y^2+y-2 = 0
The left hand side factors into a product with two terms:
(y-1) (y+2) = 0
Split into two equations:
y-1 = 0 or y+2 = 0
Add 1 to both sides:
y = 1 or y+2 = 0
Substitute back for y = x^2:
x^2 = 1 or y+2 = 0
Take the square root of both sides:
x = 1 or x = -1 or y+2 = 0
Subtract 2 from both sides:
x = 1 or x = -1 or y = -2
Substitute back for y = x^2:
x = 1 or x = -1 or x^2 = -2
Take the square root of both sides:
Answer: |x = 1 or x = -1 or x = i sqrt(2) or x = -i sqrt(2)
