x^4=-x^2-1

Solution for x^4=-x^2-1 equation:

Simplifying
x4 = -1x2 + -1

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

Solving
x4 = -1 + -1x2

Solving for variable 'x'.

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

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

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

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

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + x2 + -1 + x4 = 0 + -1

Reorder the terms:
1 + -1 + x2 + x4 = 0 + -1

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

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

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 = -1 + 0.25

Reorder the terms:
0.25 + x2 + x4 = -1 + 0.25

Combine like terms: -1 + 0.25 = -0.75
0.25 + x2 + x4 = -0.75

Factor a perfect square on the left side:
(x2 + 0.5)(x2 + 0.5) = -0.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.