S^2-2S+1=0

Solution for S^2-2S+1=0 equation:

Simplifying
S2 + -2S + 1 = 0

Reorder the terms:
1 + -2S + S2 = 0

Solving
1 + -2S + S2 = 0

Solving for variable 'S'.

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

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

Simplifying
1 + -1S = 0

Solving
1 + -1S = 0

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

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

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

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

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

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

Simplifying
1 + -1S = 0

Solving
1 + -1S = 0

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

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

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

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

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

Simplifying
S = 1
Solution
S = {1, 1}