x^4+x^2+6=0

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

Simplifying
x4 + x2 + 6 = 0

Reorder the terms:
6 + x2 + x4 = 0

Solving
6 + x2 + 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 + x2 + -6 + x4 = 0 + -6

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

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

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

The x term is x2.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x2 + 0.25 + x4 = -6 + 0.25

Reorder the terms:
0.25 + x2 + x4 = -6 + 0.25

Combine like terms: -6 + 0.25 = -5.75
0.25 + x2 + x4 = -5.75

Factor a perfect square on the left side:
(x2 + 0.5)(x2 + 0.5) = -5.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.