1=k^2(2)-k+1

Solution for 1=k^2(2)-k+1 equation:

Simplifying
1 = k2(2) + -1k + 1

Reorder the terms for easier multiplication:
1 = 2k2 + -1k + 1

Reorder the terms:
1 = 1 + -1k + 2k2

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

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

Reorder the terms:
0 = 1 + -1 + -1k + 2k2

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

Solving
0 = -1k + 2k2

Solving for variable 'k'.
Remove the zero:
k + -2k2 = -1k + 2k2 + k + -2k2

Reorder the terms:
k + -2k2 = -1k + k + 2k2 + -2k2

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

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

Factor out the Greatest Common Factor (GCF), 'k'.
k(1 + -2k) = 0

Subproblem 1
Set the factor 'k' equal to zero and attempt to solve:

Simplifying
k = 0

Solving
k = 0

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

Simplifying
k = 0
Subproblem 2
Set the factor '(1 + -2k)' equal to zero and attempt to solve:

Simplifying
1 + -2k = 0

Solving
1 + -2k = 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 + -2k = 0 + -1

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

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

Divide each side by '-2'.
k = 0.5

Simplifying
k = 0.5
Solution
k = {0, 0.5}