(6x-5)(6x-5)=11

Solution for (6x-5)(6x-5)=11 equation:

Simplifying
(6x + -5)(6x + -5) = 11

Reorder the terms:
(-5 + 6x)(6x + -5) = 11

Reorder the terms:
(-5 + 6x)(-5 + 6x) = 11

Multiply (-5 + 6x) * (-5 + 6x)
(-5(-5 + 6x) + 6x * (-5 + 6x)) = 11
((-5 * -5 + 6x * -5) + 6x * (-5 + 6x)) = 11
((25 + -30x) + 6x * (-5 + 6x)) = 11
(25 + -30x + (-5 * 6x + 6x * 6x)) = 11
(25 + -30x + (-30x + 36x2)) = 11

Combine like terms: -30x + -30x = -60x
(25 + -60x + 36x2) = 11

Solving
25 + -60x + 36x2 = 11

Solving for variable 'x'.

Reorder the terms:
25 + -11 + -60x + 36x2 = 11 + -11

Combine like terms: 25 + -11 = 14
14 + -60x + 36x2 = 11 + -11

Combine like terms: 11 + -11 = 0
14 + -60x + 36x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + -30x + 18x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(7 + -30x + 18x2)' equal to zero and attempt to solve:

Simplifying
7 + -30x + 18x2 = 0

Solving
7 + -30x + 18x2 = 0

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

Divide each side by '18'.
0.3888888889 + -1.666666667x + x2 = 0

Move the constant term to the right:

Add '-0.3888888889' to each side of the equation.
0.3888888889 + -1.666666667x + -0.3888888889 + x2 = 0 + -0.3888888889

Reorder the terms:
0.3888888889 + -0.3888888889 + -1.666666667x + x2 = 0 + -0.3888888889

Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000
0.0000000000 + -1.666666667x + x2 = 0 + -0.3888888889
-1.666666667x + x2 = 0 + -0.3888888889

Combine like terms: 0 + -0.3888888889 = -0.3888888889
-1.666666667x + x2 = -0.3888888889

The x term is -1.666666667x.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667x + 0.6944444447 + x2 = -0.3888888889 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = -0.3888888889 + 0.6944444447

Combine like terms: -0.3888888889 + 0.6944444447 = 0.3055555558
0.6944444447 + -1.666666667x + x2 = 0.3055555558

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = 0.3055555558

Calculate the square root of the right side: 0.552770799

Break this problem into two subproblems by setting 
(x + -0.8333333335) equal to 0.552770799 and -0.552770799.

Subproblem 1
x + -0.8333333335 = 0.552770799

Simplifying
x + -0.8333333335 = 0.552770799

Reorder the terms:
-0.8333333335 + x = 0.552770799

Solving
-0.8333333335 + x = 0.552770799

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = 0.552770799 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = 0.552770799 + 0.8333333335
x = 0.552770799 + 0.8333333335

Combine like terms: 0.552770799 + 0.8333333335 = 1.3861041325
x = 1.3861041325

Simplifying
x = 1.3861041325

Subproblem 2
x + -0.8333333335 = -0.552770799

Simplifying
x + -0.8333333335 = -0.552770799

Reorder the terms:
-0.8333333335 + x = -0.552770799

Solving
-0.8333333335 + x = -0.552770799

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = -0.552770799 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = -0.552770799 + 0.8333333335
x = -0.552770799 + 0.8333333335

Combine like terms: -0.552770799 + 0.8333333335 = 0.2805625345
x = 0.2805625345

Simplifying
x = 0.2805625345

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.3861041325, 0.2805625345}
Solution
x = {1.3861041325, 0.2805625345}