22x^2-44x+12=0

Solution for 22x^2-44x+12=0 equation:

Simplifying
22x2 + -44x + 12 = 0

Reorder the terms:
12 + -44x + 22x2 = 0

Solving
12 + -44x + 22x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -22x + 11x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + -22x + 11x2)' equal to zero and attempt to solve:

Simplifying
6 + -22x + 11x2 = 0

Solving
6 + -22x + 11x2 = 0

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

Divide each side by '11'.
0.5454545455 + -2x + x2 = 0

Move the constant term to the right:

Add '-0.5454545455' to each side of the equation.
0.5454545455 + -2x + -0.5454545455 + x2 = 0 + -0.5454545455

Reorder the terms:
0.5454545455 + -0.5454545455 + -2x + x2 = 0 + -0.5454545455

Combine like terms: 0.5454545455 + -0.5454545455 = 0.0000000000
0.0000000000 + -2x + x2 = 0 + -0.5454545455
-2x + x2 = 0 + -0.5454545455

Combine like terms: 0 + -0.5454545455 = -0.5454545455
-2x + x2 = -0.5454545455

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -0.5454545455 + 1

Reorder the terms:
1 + -2x + x2 = -0.5454545455 + 1

Combine like terms: -0.5454545455 + 1 = 0.4545454545
1 + -2x + x2 = 0.4545454545

Factor a perfect square on the left side:
(x + -1)(x + -1) = 0.4545454545

Calculate the square root of the right side: 0.674199862

Break this problem into two subproblems by setting 
(x + -1) equal to 0.674199862 and -0.674199862.

Subproblem 1
x + -1 = 0.674199862

Simplifying
x + -1 = 0.674199862

Reorder the terms:
-1 + x = 0.674199862

Solving
-1 + x = 0.674199862

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 0.674199862 + 1

Combine like terms: -1 + 1 = 0
0 + x = 0.674199862 + 1
x = 0.674199862 + 1

Combine like terms: 0.674199862 + 1 = 1.674199862
x = 1.674199862

Simplifying
x = 1.674199862

Subproblem 2
x + -1 = -0.674199862

Simplifying
x + -1 = -0.674199862

Reorder the terms:
-1 + x = -0.674199862

Solving
-1 + x = -0.674199862

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -0.674199862 + 1

Combine like terms: -1 + 1 = 0
0 + x = -0.674199862 + 1
x = -0.674199862 + 1

Combine like terms: -0.674199862 + 1 = 0.325800138
x = 0.325800138

Simplifying
x = 0.325800138

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.674199862, 0.325800138}
Solution
x = {1.674199862, 0.325800138}