x^2-12x+8=0

Solution for x^2-12x+8=0 equation:

Simplifying
x2 + -12x + 8 = 0

Reorder the terms:
8 + -12x + x2 = 0

Solving
8 + -12x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -12x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + -12x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -12x + x2 = 0 + -8
-12x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-12x + x2 = -8

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = -8 + 36

Reorder the terms:
36 + -12x + x2 = -8 + 36

Combine like terms: -8 + 36 = 28
36 + -12x + x2 = 28

Factor a perfect square on the left side:
(x + -6)(x + -6) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(x + -6) equal to 5.291502622 and -5.291502622.

Subproblem 1
x + -6 = 5.291502622

Simplifying
x + -6 = 5.291502622

Reorder the terms:
-6 + x = 5.291502622

Solving
-6 + x = 5.291502622

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = 5.291502622 + 6

Combine like terms: -6 + 6 = 0
0 + x = 5.291502622 + 6
x = 5.291502622 + 6

Combine like terms: 5.291502622 + 6 = 11.291502622
x = 11.291502622

Simplifying
x = 11.291502622

Subproblem 2
x + -6 = -5.291502622

Simplifying
x + -6 = -5.291502622

Reorder the terms:
-6 + x = -5.291502622

Solving
-6 + x = -5.291502622

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = -5.291502622 + 6

Combine like terms: -6 + 6 = 0
0 + x = -5.291502622 + 6
x = -5.291502622 + 6

Combine like terms: -5.291502622 + 6 = 0.708497378
x = 0.708497378

Simplifying
x = 0.708497378

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.291502622, 0.708497378}