x^4+2x^2+6=0

Solution for x^4+2x^2+6=0 equation:

Simplifying
x4 + 2x2 + 6 = 0

Reorder the terms:
6 + 2x2 + x4 = 0

Solving
6 + 2x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 2x2 + -6 + x4 = 0 + -6

Reorder the terms:
6 + -6 + 2x2 + x4 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 2x2 + x4 = 0 + -6
2x2 + x4 = 0 + -6

Combine like terms: 0 + -6 = -6
2x2 + x4 = -6

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 = -6 + 1

Reorder the terms:
1 + 2x2 + x4 = -6 + 1

Combine like terms: -6 + 1 = -5
1 + 2x2 + x4 = -5

Factor a perfect square on the left side:
(x2 + 1)(x2 + 1) = -5

Can't calculate square root of the right side.

The solution to this equation could not be determined.