x^4+8x^2-256=0

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Solution for x^4+8x^2-256=0 equation: 


Simplifying
x4 + 8x2 + -256 = 0

Reorder the terms:
-256 + 8x2 + x4 = 0

Solving
-256 + 8x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '256' to each side of the equation.
-256 + 8x2 + 256 + x4 = 0 + 256

Reorder the terms:
-256 + 256 + 8x2 + x4 = 0 + 256

Combine like terms: -256 + 256 = 0
0 + 8x2 + x4 = 0 + 256
8x2 + x4 = 0 + 256

Combine like terms: 0 + 256 = 256
8x2 + x4 = 256

The x term is 8x2.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x2 + 16 + x4 = 256 + 16

Reorder the terms:
16 + 8x2 + x4 = 256 + 16

Combine like terms: 256 + 16 = 272
16 + 8x2 + x4 = 272

Factor a perfect square on the left side:
(x2 + 4)(x2 + 4) = 272

Calculate the square root of the right side: 16.492422502

Break this problem into two subproblems by setting 
(x2 + 4) equal to 16.492422502 and -16.492422502.


Subproblem 1
x2 + 4 = 16.492422502

Simplifying
x2 + 4 = 16.492422502

Reorder the terms:
4 + x2 = 16.492422502

Solving
4 + x2 = 16.492422502

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x2 = 16.492422502 + -4

Combine like terms: 4 + -4 = 0
0 + x2 = 16.492422502 + -4
x2 = 16.492422502 + -4

Combine like terms: 16.492422502 + -4 = 12.492422502
x2 = 12.492422502

Simplifying
x2 = 12.492422502

Take the square root of each side:
x = {-3.534462123, 3.534462123}


Subproblem 2
x2 + 4 = -16.492422502

Simplifying
x2 + 4 = -16.492422502

Reorder the terms:
4 + x2 = -16.492422502

Solving
4 + x2 = -16.492422502

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x2 = -16.492422502 + -4

Combine like terms: 4 + -4 = 0
0 + x2 = -16.492422502 + -4
x2 = -16.492422502 + -4

Combine like terms: -16.492422502 + -4 = -20.492422502
x2 = -20.492422502

Simplifying
x2 = -20.492422502

Reorder the terms:
20.492422502 + x2 = -20.492422502 + 20.492422502

Combine like terms: -20.492422502 + 20.492422502 = 0.000000000
20.492422502 + 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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