(13x-6)(13x-6)=117

Solution for (13x-6)(13x-6)=117 equation:

Simplifying
(13x + -6)(13x + -6) = 117

Reorder the terms:
(-6 + 13x)(13x + -6) = 117

Reorder the terms:
(-6 + 13x)(-6 + 13x) = 117

Multiply (-6 + 13x) * (-6 + 13x)
(-6(-6 + 13x) + 13x * (-6 + 13x)) = 117
((-6 * -6 + 13x * -6) + 13x * (-6 + 13x)) = 117
((36 + -78x) + 13x * (-6 + 13x)) = 117
(36 + -78x + (-6 * 13x + 13x * 13x)) = 117
(36 + -78x + (-78x + 169x2)) = 117

Combine like terms: -78x + -78x = -156x
(36 + -156x + 169x2) = 117

Solving
36 + -156x + 169x2 = 117

Solving for variable 'x'.

Reorder the terms:
36 + -117 + -156x + 169x2 = 117 + -117

Combine like terms: 36 + -117 = -81
-81 + -156x + 169x2 = 117 + -117

Combine like terms: 117 + -117 = 0
-81 + -156x + 169x2 = 0

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

Divide each side by '169'.
-0.4792899408 + -0.9230769231x + x2 = 0

Move the constant term to the right:

Add '0.4792899408' to each side of the equation.
-0.4792899408 + -0.9230769231x + 0.4792899408 + x2 = 0 + 0.4792899408

Reorder the terms:
-0.4792899408 + 0.4792899408 + -0.9230769231x + x2 = 0 + 0.4792899408

Combine like terms: -0.4792899408 + 0.4792899408 = 0.0000000000
0.0000000000 + -0.9230769231x + x2 = 0 + 0.4792899408
-0.9230769231x + x2 = 0 + 0.4792899408

Combine like terms: 0 + 0.4792899408 = 0.4792899408
-0.9230769231x + x2 = 0.4792899408

The x term is -0.9230769231x.  Take half its coefficient (-0.4615384616).
Square it (0.2130177515) and add it to both sides.

Add '0.2130177515' to each side of the equation.
-0.9230769231x + 0.2130177515 + x2 = 0.4792899408 + 0.2130177515

Reorder the terms:
0.2130177515 + -0.9230769231x + x2 = 0.4792899408 + 0.2130177515

Combine like terms: 0.4792899408 + 0.2130177515 = 0.6923076923
0.2130177515 + -0.9230769231x + x2 = 0.6923076923

Factor a perfect square on the left side:
(x + -0.4615384616)(x + -0.4615384616) = 0.6923076923

Calculate the square root of the right side: 0.832050294

Break this problem into two subproblems by setting 
(x + -0.4615384616) equal to 0.832050294 and -0.832050294.

Subproblem 1
x + -0.4615384616 = 0.832050294

Simplifying
x + -0.4615384616 = 0.832050294

Reorder the terms:
-0.4615384616 + x = 0.832050294

Solving
-0.4615384616 + x = 0.832050294

Solving for variable 'x'.

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

Add '0.4615384616' to each side of the equation.
-0.4615384616 + 0.4615384616 + x = 0.832050294 + 0.4615384616

Combine like terms: -0.4615384616 + 0.4615384616 = 0.0000000000
0.0000000000 + x = 0.832050294 + 0.4615384616
x = 0.832050294 + 0.4615384616

Combine like terms: 0.832050294 + 0.4615384616 = 1.2935887556
x = 1.2935887556

Simplifying
x = 1.2935887556

Subproblem 2
x + -0.4615384616 = -0.832050294

Simplifying
x + -0.4615384616 = -0.832050294

Reorder the terms:
-0.4615384616 + x = -0.832050294

Solving
-0.4615384616 + x = -0.832050294

Solving for variable 'x'.

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

Add '0.4615384616' to each side of the equation.
-0.4615384616 + 0.4615384616 + x = -0.832050294 + 0.4615384616

Combine like terms: -0.4615384616 + 0.4615384616 = 0.0000000000
0.0000000000 + x = -0.832050294 + 0.4615384616
x = -0.832050294 + 0.4615384616

Combine like terms: -0.832050294 + 0.4615384616 = -0.3705118324
x = -0.3705118324

Simplifying
x = -0.3705118324

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.2935887556, -0.3705118324}