K^4-2K^2+1=

Solution for K^4-2K^2+1= equation:

Simplifying
K4 + -2K2 + 1 = 0

Reorder the terms:
1 + -2K2 + K4 = 0

Solving
1 + -2K2 + K4 = 0

Solving for variable 'K'.

Factor a trinomial.
(1 + -1K2)(1 + -1K2) = 0

Factor a difference between two squares.
((1 + K)(1 + -1K))(1 + -1K2) = 0

Factor a difference between two squares.
((1 + K)(1 + -1K))(1 + K)(1 + -1K) = 0

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

Simplifying
1 + K = 0

Solving
1 + K = 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 + K = 0 + -1

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

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

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

Simplifying
1 + -1K = 0

Solving
1 + -1K = 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 + -1K = 0 + -1

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

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

Divide each side by '-1'.
K = 1

Simplifying
K = 1
Subproblem 3
Set the factor '(1 + K)' equal to zero and attempt to solve:

Simplifying
1 + K = 0

Solving
1 + K = 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 + K = 0 + -1

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

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

Simplifying
K = -1
Subproblem 4
Set the factor '(1 + -1K)' equal to zero and attempt to solve:

Simplifying
1 + -1K = 0

Solving
1 + -1K = 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 + -1K = 0 + -1

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

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

Divide each side by '-1'.
K = 1

Simplifying
K = 1
Solution
K = {-1, 1, -1, 1}