9x^2-9x+1=12

Solution for 9x^2-9x+1=12 equation:

Simplifying
9x2 + -9x + 1 = 12

Reorder the terms:
1 + -9x + 9x2 = 12

Solving
1 + -9x + 9x2 = 12

Solving for variable 'x'.

Reorder the terms:
1 + -12 + -9x + 9x2 = 12 + -12

Combine like terms: 1 + -12 = -11
-11 + -9x + 9x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-11 + -9x + 9x2 = 0

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

Divide each side by '9'.
-1.222222222 + -1x + x2 = 0

Move the constant term to the right:

Add '1.222222222' to each side of the equation.
-1.222222222 + -1x + 1.222222222 + x2 = 0 + 1.222222222

Reorder the terms:
-1.222222222 + 1.222222222 + -1x + x2 = 0 + 1.222222222

Combine like terms: -1.222222222 + 1.222222222 = 0.000000000
0.000000000 + -1x + x2 = 0 + 1.222222222
-1x + x2 = 0 + 1.222222222

Combine like terms: 0 + 1.222222222 = 1.222222222
-1x + x2 = 1.222222222

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 = 1.222222222 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 1.222222222 + 0.25

Combine like terms: 1.222222222 + 0.25 = 1.472222222
0.25 + -1x + x2 = 1.472222222

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 1.472222222

Calculate the square root of the right side: 1.213351648

Break this problem into two subproblems by setting 
(x + -0.5) equal to 1.213351648 and -1.213351648.

Subproblem 1
x + -0.5 = 1.213351648

Simplifying
x + -0.5 = 1.213351648

Reorder the terms:
-0.5 + x = 1.213351648

Solving
-0.5 + x = 1.213351648

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 = 1.213351648 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 1.213351648 + 0.5
x = 1.213351648 + 0.5

Combine like terms: 1.213351648 + 0.5 = 1.713351648
x = 1.713351648

Simplifying
x = 1.713351648

Subproblem 2
x + -0.5 = -1.213351648

Simplifying
x + -0.5 = -1.213351648

Reorder the terms:
-0.5 + x = -1.213351648

Solving
-0.5 + x = -1.213351648

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 = -1.213351648 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -1.213351648 + 0.5
x = -1.213351648 + 0.5

Combine like terms: -1.213351648 + 0.5 = -0.713351648
x = -0.713351648

Simplifying
x = -0.713351648

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.713351648, -0.713351648}