x^4+8x^2=-8

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


Simplifying
x4 + 8x2 = -8

Reorder the terms:
8x2 + x4 = -8

Solving
8x2 + x4 = -8

Solving for variable 'x'.

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

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -8 + 16

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

Combine like terms: -8 + 16 = 8
16 + 8x2 + x4 = 8

Factor a perfect square on the left side:
(x2 + 4)(x2 + 4) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(x2 + 4) equal to 2.828427125 and -2.828427125.


Subproblem 1
x2 + 4 = 2.828427125

Simplifying
x2 + 4 = 2.828427125

Reorder the terms:
4 + x2 = 2.828427125

Solving
4 + x2 = 2.828427125

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 = 2.828427125 + -4

Combine like terms: 4 + -4 = 0
0 + x2 = 2.828427125 + -4
x2 = 2.828427125 + -4

Combine like terms: 2.828427125 + -4 = -1.171572875
x2 = -1.171572875

Simplifying
x2 = -1.171572875

Reorder the terms:
1.171572875 + x2 = -1.171572875 + 1.171572875

Combine like terms: -1.171572875 + 1.171572875 = 0.000000000
1.171572875 + x2 = 0.000000000

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


Subproblem 2
x2 + 4 = -2.828427125

Simplifying
x2 + 4 = -2.828427125

Reorder the terms:
4 + x2 = -2.828427125

Solving
4 + x2 = -2.828427125

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 = -2.828427125 + -4

Combine like terms: 4 + -4 = 0
0 + x2 = -2.828427125 + -4
x2 = -2.828427125 + -4

Combine like terms: -2.828427125 + -4 = -6.828427125
x2 = -6.828427125

Simplifying
x2 = -6.828427125

Reorder the terms:
6.828427125 + x2 = -6.828427125 + 6.828427125

Combine like terms: -6.828427125 + 6.828427125 = 0.000000000
6.828427125 + 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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