6x^2-66x+36=0

Solution for 6x^2-66x+36=0 equation:

Simplifying
6x2 + -66x + 36 = 0

Reorder the terms:
36 + -66x + 6x2 = 0

Solving
36 + -66x + 6x2 = 0

Solving for variable 'x'.

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

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

Simplifying
6 + -11x + x2 = 0

Solving
6 + -11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -11x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -11x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -11x + x2 = 0 + -6
-11x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-11x + x2 = -6

The x term is -11x.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x + 30.25 + x2 = -6 + 30.25

Reorder the terms:
30.25 + -11x + x2 = -6 + 30.25

Combine like terms: -6 + 30.25 = 24.25
30.25 + -11x + x2 = 24.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(x + -5.5) equal to 4.924428901 and -4.924428901.

Subproblem 1
x + -5.5 = 4.924428901

Simplifying
x + -5.5 = 4.924428901

Reorder the terms:
-5.5 + x = 4.924428901

Solving
-5.5 + x = 4.924428901

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = 4.924428901 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 4.924428901 + 5.5
x = 4.924428901 + 5.5

Combine like terms: 4.924428901 + 5.5 = 10.424428901
x = 10.424428901

Simplifying
x = 10.424428901

Subproblem 2
x + -5.5 = -4.924428901

Simplifying
x + -5.5 = -4.924428901

Reorder the terms:
-5.5 + x = -4.924428901

Solving
-5.5 + x = -4.924428901

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = -4.924428901 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -4.924428901 + 5.5
x = -4.924428901 + 5.5

Combine like terms: -4.924428901 + 5.5 = 0.575571099
x = 0.575571099

Simplifying
x = 0.575571099

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.424428901, 0.575571099}
Solution
x = {10.424428901, 0.575571099}