Solve for x:
x^6 - 2 x^4 - x^2 + 2 = 0
The left hand side factors into a product with four terms:
(x - 1) (x + 1) (x^2 - 2) (x^2 + 1) = 0
Split into four equations:
x - 1 = 0 or x + 1 = 0 or x^2 - 2 = 0 or x^2 + 1 = 0
Add 1 to both sides:
x = 1 or x + 1 = 0 or x^2 - 2 = 0 or x^2 + 1 = 0
Subtract 1 from both sides:
x = 1 or x = -1 or x^2 - 2 = 0 or x^2 + 1 = 0
Add 2 to both sides:
x = 1 or x = -1 or x^2 = 2 or x^2 + 1 = 0
Take the square root of both sides:
x = 1 or x = -1 or x = sqrt(2) or x = -sqrt(2) or x^2 + 1 = 0
Subtract 1 from both sides:
x = 1 or x = -1 or x = sqrt(2) or x = -sqrt(2) or x^2 = -1
Take the square root of both sides:
x = 1 or x = -1 or x = sqrt(2) or x = -sqrt(2)