x^4+16x^2-256=0

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Solution for x^4+16x^2-256=0 equation: 


Simplifying
x4 + 16x2 + -256 = 0

Reorder the terms:
-256 + 16x2 + x4 = 0

Solving
-256 + 16x2 + 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 + 16x2 + 256 + x4 = 0 + 256

Reorder the terms:
-256 + 256 + 16x2 + x4 = 0 + 256

Combine like terms: -256 + 256 = 0
0 + 16x2 + x4 = 0 + 256
16x2 + x4 = 0 + 256

Combine like terms: 0 + 256 = 256
16x2 + x4 = 256

The x term is 16x2.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x2 + 64 + x4 = 256 + 64

Reorder the terms:
64 + 16x2 + x4 = 256 + 64

Combine like terms: 256 + 64 = 320
64 + 16x2 + x4 = 320

Factor a perfect square on the left side:
(x2 + 8)(x2 + 8) = 320

Calculate the square root of the right side: 17.88854382

Break this problem into two subproblems by setting 
(x2 + 8) equal to 17.88854382 and -17.88854382.


Subproblem 1
x2 + 8 = 17.88854382

Simplifying
x2 + 8 = 17.88854382

Reorder the terms:
8 + x2 = 17.88854382

Solving
8 + x2 = 17.88854382

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x2 = 17.88854382 + -8

Combine like terms: 8 + -8 = 0
0 + x2 = 17.88854382 + -8
x2 = 17.88854382 + -8

Combine like terms: 17.88854382 + -8 = 9.88854382
x2 = 9.88854382

Simplifying
x2 = 9.88854382

Take the square root of each side:
x = {-3.144605511, 3.144605511}


Subproblem 2
x2 + 8 = -17.88854382

Simplifying
x2 + 8 = -17.88854382

Reorder the terms:
8 + x2 = -17.88854382

Solving
8 + x2 = -17.88854382

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x2 = -17.88854382 + -8

Combine like terms: 8 + -8 = 0
0 + x2 = -17.88854382 + -8
x2 = -17.88854382 + -8

Combine like terms: -17.88854382 + -8 = -25.88854382
x2 = -25.88854382

Simplifying
x2 = -25.88854382

Reorder the terms:
25.88854382 + x2 = -25.88854382 + 25.88854382

Combine like terms: -25.88854382 + 25.88854382 = 0.00000000
25.88854382 + x2 = 0.00000000

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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