0=x^4+2x^2+4

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

Simplifying
0 = x4 + 2x2 + 4

Reorder the terms:
0 = 4 + 2x2 + x4

Solving
0 = 4 + 2x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + -4 = -4
-4 + -2x2 + -1x4 = 4 + 2x2 + x4 + -4 + -2x2 + -1x4

Reorder the terms:
-4 + -2x2 + -1x4 = 4 + -4 + 2x2 + -2x2 + x4 + -1x4

Combine like terms: 4 + -4 = 0
-4 + -2x2 + -1x4 = 0 + 2x2 + -2x2 + x4 + -1x4
-4 + -2x2 + -1x4 = 2x2 + -2x2 + x4 + -1x4

Combine like terms: 2x2 + -2x2 = 0
-4 + -2x2 + -1x4 = 0 + x4 + -1x4
-4 + -2x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-4 + -2x2 + -1x4 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 2x2 + x4) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(4 + 2x2 + x4)' equal to zero and attempt to solve:

Simplifying
4 + 2x2 + x4 = 0

Solving
4 + 2x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 2x2 + -4 + x4 = 0 + -4

Reorder the terms:
4 + -4 + 2x2 + x4 = 0 + -4

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

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

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 = -4 + 1

Reorder the terms:
1 + 2x2 + x4 = -4 + 1

Combine like terms: -4 + 1 = -3
1 + 2x2 + x4 = -3

Factor a perfect square on the left side:
(x2 + 1)(x2 + 1) = -3

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.