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

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


Simplifying
x4 + 16x2 + -16 = 0

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

Solving
-16 + 16x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 16x2 + 16 + x4 = 0 + 16

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

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

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

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 = 16 + 64

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

Combine like terms: 16 + 64 = 80
64 + 16x2 + x4 = 80

Factor a perfect square on the left side:
(x2 + 8)(x2 + 8) = 80

Calculate the square root of the right side: 8.94427191

Break this problem into two subproblems by setting 
(x2 + 8) equal to 8.94427191 and -8.94427191.


Subproblem 1
x2 + 8 = 8.94427191

Simplifying
x2 + 8 = 8.94427191

Reorder the terms:
8 + x2 = 8.94427191

Solving
8 + x2 = 8.94427191

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 = 8.94427191 + -8

Combine like terms: 8 + -8 = 0
0 + x2 = 8.94427191 + -8
x2 = 8.94427191 + -8

Combine like terms: 8.94427191 + -8 = 0.94427191
x2 = 0.94427191

Simplifying
x2 = 0.94427191

Take the square root of each side:
x = {-0.971736544, 0.971736544}


Subproblem 2
x2 + 8 = -8.94427191

Simplifying
x2 + 8 = -8.94427191

Reorder the terms:
8 + x2 = -8.94427191

Solving
8 + x2 = -8.94427191

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 = -8.94427191 + -8

Combine like terms: 8 + -8 = 0
0 + x2 = -8.94427191 + -8
x2 = -8.94427191 + -8

Combine like terms: -8.94427191 + -8 = -16.94427191
x2 = -16.94427191

Simplifying
x2 = -16.94427191

Reorder the terms:
16.94427191 + x2 = -16.94427191 + 16.94427191

Combine like terms: -16.94427191 + 16.94427191 = 0.00000000
16.94427191 + 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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