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

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Solution for x^4-32x^2-4=0 equation: 


Simplifying
x4 + -32x2 + -4 = 0

Reorder the terms:
-4 + -32x2 + x4 = 0

Solving
-4 + -32x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -32x2 + 4 + x4 = 0 + 4

Reorder the terms:
-4 + 4 + -32x2 + x4 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -32x2 + x4 = 0 + 4
-32x2 + x4 = 0 + 4

Combine like terms: 0 + 4 = 4
-32x2 + x4 = 4

The x term is -32x2.  Take half its coefficient (-16).
Square it (256) and add it to both sides.

Add '256' to each side of the equation.
-32x2 + 256 + x4 = 4 + 256

Reorder the terms:
256 + -32x2 + x4 = 4 + 256

Combine like terms: 4 + 256 = 260
256 + -32x2 + x4 = 260

Factor a perfect square on the left side:
(x2 + -16)(x2 + -16) = 260

Calculate the square root of the right side: 16.124515497

Break this problem into two subproblems by setting 
(x2 + -16) equal to 16.124515497 and -16.124515497.


Subproblem 1
x2 + -16 = 16.124515497

Simplifying
x2 + -16 = 16.124515497

Reorder the terms:
-16 + x2 = 16.124515497

Solving
-16 + x2 = 16.124515497

Solving for variable 'x'.

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

Add '16' to each side of the equation.
-16 + 16 + x2 = 16.124515497 + 16

Combine like terms: -16 + 16 = 0
0 + x2 = 16.124515497 + 16
x2 = 16.124515497 + 16

Combine like terms: 16.124515497 + 16 = 32.124515497
x2 = 32.124515497

Simplifying
x2 = 32.124515497

Take the square root of each side:
x = {-5.667849283, 5.667849283}


Subproblem 2
x2 + -16 = -16.124515497

Simplifying
x2 + -16 = -16.124515497

Reorder the terms:
-16 + x2 = -16.124515497

Solving
-16 + x2 = -16.124515497

Solving for variable 'x'.

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

Add '16' to each side of the equation.
-16 + 16 + x2 = -16.124515497 + 16

Combine like terms: -16 + 16 = 0
0 + x2 = -16.124515497 + 16
x2 = -16.124515497 + 16

Combine like terms: -16.124515497 + 16 = -0.124515497
x2 = -0.124515497

Simplifying
x2 = -0.124515497

Reorder the terms:
0.124515497 + x2 = -0.124515497 + 0.124515497

Combine like terms: -0.124515497 + 0.124515497 = 0.000000000
0.124515497 + 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.

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