(7x-5)(7x-5)=186

Solution for (7x-5)(7x-5)=186 equation:

Simplifying
(7x + -5)(7x + -5) = 186

Reorder the terms:
(-5 + 7x)(7x + -5) = 186

Reorder the terms:
(-5 + 7x)(-5 + 7x) = 186

Multiply (-5 + 7x) * (-5 + 7x)
(-5(-5 + 7x) + 7x * (-5 + 7x)) = 186
((-5 * -5 + 7x * -5) + 7x * (-5 + 7x)) = 186
((25 + -35x) + 7x * (-5 + 7x)) = 186
(25 + -35x + (-5 * 7x + 7x * 7x)) = 186
(25 + -35x + (-35x + 49x2)) = 186

Combine like terms: -35x + -35x = -70x
(25 + -70x + 49x2) = 186

Solving
25 + -70x + 49x2 = 186

Solving for variable 'x'.

Reorder the terms:
25 + -186 + -70x + 49x2 = 186 + -186

Combine like terms: 25 + -186 = -161
-161 + -70x + 49x2 = 186 + -186

Combine like terms: 186 + -186 = 0
-161 + -70x + 49x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-23 + -10x + 7x2) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-23 + -10x + 7x2)' equal to zero and attempt to solve:

Simplifying
-23 + -10x + 7x2 = 0

Solving
-23 + -10x + 7x2 = 0

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

Divide each side by '7'.
-3.285714286 + -1.428571429x + x2 = 0

Move the constant term to the right:

Add '3.285714286' to each side of the equation.
-3.285714286 + -1.428571429x + 3.285714286 + x2 = 0 + 3.285714286

Reorder the terms:
-3.285714286 + 3.285714286 + -1.428571429x + x2 = 0 + 3.285714286

Combine like terms: -3.285714286 + 3.285714286 = 0.000000000
0.000000000 + -1.428571429x + x2 = 0 + 3.285714286
-1.428571429x + x2 = 0 + 3.285714286

Combine like terms: 0 + 3.285714286 = 3.285714286
-1.428571429x + x2 = 3.285714286

The x term is -1.428571429x.  Take half its coefficient (-0.7142857145).
Square it (0.5102040819) and add it to both sides.

Add '0.5102040819' to each side of the equation.
-1.428571429x + 0.5102040819 + x2 = 3.285714286 + 0.5102040819

Reorder the terms:
0.5102040819 + -1.428571429x + x2 = 3.285714286 + 0.5102040819

Combine like terms: 3.285714286 + 0.5102040819 = 3.7959183679
0.5102040819 + -1.428571429x + x2 = 3.7959183679

Factor a perfect square on the left side:
(x + -0.7142857145)(x + -0.7142857145) = 3.7959183679

Calculate the square root of the right side: 1.948311671

Break this problem into two subproblems by setting 
(x + -0.7142857145) equal to 1.948311671 and -1.948311671.

Subproblem 1
x + -0.7142857145 = 1.948311671

Simplifying
x + -0.7142857145 = 1.948311671

Reorder the terms:
-0.7142857145 + x = 1.948311671

Solving
-0.7142857145 + x = 1.948311671

Solving for variable 'x'.

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

Add '0.7142857145' to each side of the equation.
-0.7142857145 + 0.7142857145 + x = 1.948311671 + 0.7142857145

Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000
0.0000000000 + x = 1.948311671 + 0.7142857145
x = 1.948311671 + 0.7142857145

Combine like terms: 1.948311671 + 0.7142857145 = 2.6625973855
x = 2.6625973855

Simplifying
x = 2.6625973855

Subproblem 2
x + -0.7142857145 = -1.948311671

Simplifying
x + -0.7142857145 = -1.948311671

Reorder the terms:
-0.7142857145 + x = -1.948311671

Solving
-0.7142857145 + x = -1.948311671

Solving for variable 'x'.

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

Add '0.7142857145' to each side of the equation.
-0.7142857145 + 0.7142857145 + x = -1.948311671 + 0.7142857145

Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000
0.0000000000 + x = -1.948311671 + 0.7142857145
x = -1.948311671 + 0.7142857145

Combine like terms: -1.948311671 + 0.7142857145 = -1.2340259565
x = -1.2340259565

Simplifying
x = -1.2340259565

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.6625973855, -1.2340259565}
Solution
x = {2.6625973855, -1.2340259565}