Z^4+Z^2+2=0

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

Simplifying
Z4 + Z2 + 2 = 0

Reorder the terms:
2 + Z2 + Z4 = 0

Solving
2 + Z2 + Z4 = 0

Solving for variable 'Z'.

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + Z2 + -2 + Z4 = 0 + -2

Reorder the terms:
2 + -2 + Z2 + Z4 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + Z2 + Z4 = 0 + -2
Z2 + Z4 = 0 + -2

Combine like terms: 0 + -2 = -2
Z2 + Z4 = -2

The Z term is Z2.  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.
Z2 + 0.25 + Z4 = -2 + 0.25

Reorder the terms:
0.25 + Z2 + Z4 = -2 + 0.25

Combine like terms: -2 + 0.25 = -1.75
0.25 + Z2 + Z4 = -1.75

Factor a perfect square on the left side:
(Z2 + 0.5)(Z2 + 0.5) = -1.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.