x^4+8x^2-33=0

Solution for x^4+8x^2-33=0 equation:

Simplifying
x4 + 8x2 + -33 = 0

Reorder the terms:
-33 + 8x2 + x4 = 0

Solving
-33 + 8x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-11 + -1x2)(3 + -1x2) = 0

Subproblem 1
Set the factor '(-11 + -1x2)' equal to zero and attempt to solve:

Simplifying
-11 + -1x2 = 0

Solving
-11 + -1x2 = 0

Move all terms containing x to the left, all other terms to the right.

Add '11' to each side of the equation.
-11 + 11 + -1x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1x2 = 0 + 11
-1x2 = 0 + 11

Combine like terms: 0 + 11 = 11
-1x2 = 11

Divide each side by '-1'.
x2 = -11

Simplifying
x2 = -11

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(3 + -1x2)' equal to zero and attempt to solve:

Simplifying
3 + -1x2 = 0

Solving
3 + -1x2 = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x2 = 0 + -3
-1x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1x2 = -3

Divide each side by '-1'.
x2 = 3

Simplifying
x2 = 3

Take the square root of each side:
x = {-1.732050808, 1.732050808}
Solution
x = {-1.732050808, 1.732050808}