k^6+k^3=-6

Solution for k^6+k^3=-6 equation:

Simplifying
k6 + k3 = -6

Reorder the terms:
k3 + k6 = -6

Solving
k3 + k6 = -6

Solving for variable 'k'.

Reorder the terms:
6 + k3 + k6 = -6 + 6

Combine like terms: -6 + 6 = 0
6 + k3 + k6 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + k3 + -6 + k6 = 0 + -6

Reorder the terms:
6 + -6 + k3 + k6 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + k3 + k6 = 0 + -6
k3 + k6 = 0 + -6

Combine like terms: 0 + -6 = -6
k3 + k6 = -6

The k term is k3.  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.
k3 + 0.25 + k6 = -6 + 0.25

Reorder the terms:
0.25 + k3 + k6 = -6 + 0.25

Combine like terms: -6 + 0.25 = -5.75
0.25 + k3 + k6 = -5.75

Factor a perfect square on the left side:
(k3 + 0.5)(k3 + 0.5) = -5.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.