k^4-5k^2+6=0

Solution for k^4-5k^2+6=0 equation:

Simplifying
k4 + -5k2 + 6 = 0

Reorder the terms:
6 + -5k2 + k4 = 0

Solving
6 + -5k2 + k4 = 0

Solving for variable 'k'.

Factor a trinomial.
(2 + -1k2)(3 + -1k2) = 0

Subproblem 1
Set the factor '(2 + -1k2)' equal to zero and attempt to solve:

Simplifying
2 + -1k2 = 0

Solving
2 + -1k2 = 0

Move all terms containing k to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1k2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1k2 = 0 + -2
-1k2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1k2 = -2

Divide each side by '-1'.
k2 = 2

Simplifying
k2 = 2

Take the square root of each side:
k = {-1.414213562, 1.414213562}
Subproblem 2
Set the factor '(3 + -1k2)' equal to zero and attempt to solve:

Simplifying
3 + -1k2 = 0

Solving
3 + -1k2 = 0

Move all terms containing k to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1k2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1k2 = 0 + -3
-1k2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1k2 = -3

Divide each side by '-1'.
k2 = 3

Simplifying
k2 = 3

Take the square root of each side:
k = {-1.732050808, 1.732050808}
Solution
k = {-1.414213562, 1.414213562, -1.732050808, 1.732050808}