x^4-4x^2+4+x^4+8x^2+16-4=0

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Solution for x^4-4x^2+4+x^4+8x^2+16-4=0 equation: 


Simplifying
x4 + -4x2 + 4 + x4 + 8x2 + 16 + -4 = 0

Reorder the terms:
4 + 16 + -4 + -4x2 + 8x2 + x4 + x4 = 0

Combine like terms: 4 + 16 = 20
20 + -4 + -4x2 + 8x2 + x4 + x4 = 0

Combine like terms: 20 + -4 = 16
16 + -4x2 + 8x2 + x4 + x4 = 0

Combine like terms: -4x2 + 8x2 = 4x2
16 + 4x2 + x4 + x4 = 0

Combine like terms: x4 + x4 = 2x4
16 + 4x2 + 2x4 = 0

Solving
16 + 4x2 + 2x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + 2x2 + x4) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(8 + 2x2 + x4)' equal to zero and attempt to solve:

Simplifying
8 + 2x2 + x4 = 0

Solving
8 + 2x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 2x2 + -8 + x4 = 0 + -8

Reorder the terms:
8 + -8 + 2x2 + x4 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 2x2 + x4 = 0 + -8
2x2 + x4 = 0 + -8

Combine like terms: 0 + -8 = -8
2x2 + x4 = -8

The x term is 2x2.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x2 + 1 + x4 = -8 + 1

Reorder the terms:
1 + 2x2 + x4 = -8 + 1

Combine like terms: -8 + 1 = -7
1 + 2x2 + x4 = -7

Factor a perfect square on the left side:
(x2 + 1)(x2 + 1) = -7

Can't calculate square root of the right side.

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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