12x^2-12x+1=0

Solution for 12x^2-12x+1=0 equation:

Simplifying
12x2 + -12x + 1 = 0

Reorder the terms:
1 + -12x + 12x2 = 0

Solving
1 + -12x + 12x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
12 the coefficient of the squared term: 

Divide each side by '12'.
0.08333333333 + -1x + x2 = 0

Move the constant term to the right:

Add '-0.08333333333' to each side of the equation.
0.08333333333 + -1x + -0.08333333333 + x2 = 0 + -0.08333333333

Reorder the terms:
0.08333333333 + -0.08333333333 + -1x + x2 = 0 + -0.08333333333

Combine like terms: 0.08333333333 + -0.08333333333 = 0.00000000000
0.00000000000 + -1x + x2 = 0 + -0.08333333333
-1x + x2 = 0 + -0.08333333333

Combine like terms: 0 + -0.08333333333 = -0.08333333333
-1x + x2 = -0.08333333333

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -0.08333333333 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -0.08333333333 + 0.25

Combine like terms: -0.08333333333 + 0.25 = 0.16666666667
0.25 + -1x + x2 = 0.16666666667

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.16666666667

Calculate the square root of the right side: 0.40824829

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.40824829 and -0.40824829.

Subproblem 1
x + -0.5 = 0.40824829

Simplifying
x + -0.5 = 0.40824829

Reorder the terms:
-0.5 + x = 0.40824829

Solving
-0.5 + x = 0.40824829

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 0.40824829 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 0.40824829 + 0.5
x = 0.40824829 + 0.5

Combine like terms: 0.40824829 + 0.5 = 0.90824829
x = 0.90824829

Simplifying
x = 0.90824829

Subproblem 2
x + -0.5 = -0.40824829

Simplifying
x + -0.5 = -0.40824829

Reorder the terms:
-0.5 + x = -0.40824829

Solving
-0.5 + x = -0.40824829

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -0.40824829 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -0.40824829 + 0.5
x = -0.40824829 + 0.5

Combine like terms: -0.40824829 + 0.5 = 0.09175171
x = 0.09175171

Simplifying
x = 0.09175171

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.90824829, 0.09175171}