x^4+x^2-33=0

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

Simplifying
x4 + x2 + -33 = 0

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

Solving
-33 + x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '33' to each side of the equation.
-33 + x2 + 33 + x4 = 0 + 33

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

Combine like terms: -33 + 33 = 0
0 + x2 + x4 = 0 + 33
x2 + x4 = 0 + 33

Combine like terms: 0 + 33 = 33
x2 + x4 = 33

The x term is x2.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x2 + 0.25 + x4 = 33 + 0.25

Reorder the terms:
0.25 + x2 + x4 = 33 + 0.25

Combine like terms: 33 + 0.25 = 33.25
0.25 + x2 + x4 = 33.25

Factor a perfect square on the left side:
(x2 + 0.5)(x2 + 0.5) = 33.25

Calculate the square root of the right side: 5.766281297

Break this problem into two subproblems by setting 
(x2 + 0.5) equal to 5.766281297 and -5.766281297.

Subproblem 1
x2 + 0.5 = 5.766281297

Simplifying
x2 + 0.5 = 5.766281297

Reorder the terms:
0.5 + x2 = 5.766281297

Solving
0.5 + x2 = 5.766281297

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x2 = 5.766281297 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x2 = 5.766281297 + -0.5
x2 = 5.766281297 + -0.5

Combine like terms: 5.766281297 + -0.5 = 5.266281297
x2 = 5.266281297

Simplifying
x2 = 5.266281297

Take the square root of each side:
x = {-2.294837967, 2.294837967}

Subproblem 2
x2 + 0.5 = -5.766281297

Simplifying
x2 + 0.5 = -5.766281297

Reorder the terms:
0.5 + x2 = -5.766281297

Solving
0.5 + x2 = -5.766281297

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x2 = -5.766281297 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x2 = -5.766281297 + -0.5
x2 = -5.766281297 + -0.5

Combine like terms: -5.766281297 + -0.5 = -6.266281297
x2 = -6.266281297

Simplifying
x2 = -6.266281297

Reorder the terms:
6.266281297 + x2 = -6.266281297 + 6.266281297

Combine like terms: -6.266281297 + 6.266281297 = 0.000000000
6.266281297 + x2 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.