k^2x^4-2kx^2+1=0

Solution for k^2x^4-2kx^2+1=0 equation:

Simplifying
k2x4 + -2kx2 + 1 = 0

Reorder the terms:
1 + -2kx2 + k2x4 = 0

Solving
1 + -2kx2 + k2x4 = 0

Solving for variable 'k'.

Factor a trinomial.
(1 + -1kx2)(1 + -1kx2) = 0

Subproblem 1
Set the factor '(1 + -1kx2)' equal to zero and attempt to solve:

Simplifying
1 + -1kx2 = 0

Solving
1 + -1kx2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1kx2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1kx2 = 0 + -1
-1kx2 = 0 + -1

Combine like terms: 0 + -1 = -1
-1kx2 = -1

Divide each side by '-1x2'.
k = x-2

Simplifying
k = x-2
Subproblem 2
Set the factor '(1 + -1kx2)' equal to zero and attempt to solve:

Simplifying
1 + -1kx2 = 0

Solving
1 + -1kx2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1kx2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1kx2 = 0 + -1
-1kx2 = 0 + -1

Combine like terms: 0 + -1 = -1
-1kx2 = -1

Divide each side by '-1x2'.
k = x-2

Simplifying
k = x-2
Solution
k = {x-2, x-2}