(6x+2)(6x+2)=50

Solution for (6x+2)(6x+2)=50 equation:

Simplifying
(6x + 2)(6x + 2) = 50

Reorder the terms:
(2 + 6x)(6x + 2) = 50

Reorder the terms:
(2 + 6x)(2 + 6x) = 50

Multiply (2 + 6x) * (2 + 6x)
(2(2 + 6x) + 6x * (2 + 6x)) = 50
((2 * 2 + 6x * 2) + 6x * (2 + 6x)) = 50
((4 + 12x) + 6x * (2 + 6x)) = 50
(4 + 12x + (2 * 6x + 6x * 6x)) = 50
(4 + 12x + (12x + 36x2)) = 50

Combine like terms: 12x + 12x = 24x
(4 + 24x + 36x2) = 50

Solving
4 + 24x + 36x2 = 50

Solving for variable 'x'.

Reorder the terms:
4 + -50 + 24x + 36x2 = 50 + -50

Combine like terms: 4 + -50 = -46
-46 + 24x + 36x2 = 50 + -50

Combine like terms: 50 + -50 = 0
-46 + 24x + 36x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-23 + 12x + 18x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-23 + 12x + 18x2)' equal to zero and attempt to solve:

Simplifying
-23 + 12x + 18x2 = 0

Solving
-23 + 12x + 18x2 = 0

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

Divide each side by '18'.
-1.277777778 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '1.277777778' to each side of the equation.
-1.277777778 + 0.6666666667x + 1.277777778 + x2 = 0 + 1.277777778

Reorder the terms:
-1.277777778 + 1.277777778 + 0.6666666667x + x2 = 0 + 1.277777778

Combine like terms: -1.277777778 + 1.277777778 = 0.000000000
0.000000000 + 0.6666666667x + x2 = 0 + 1.277777778
0.6666666667x + x2 = 0 + 1.277777778

Combine like terms: 0 + 1.277777778 = 1.277777778
0.6666666667x + x2 = 1.277777778

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 1.277777778 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 1.277777778 + 0.1111111112

Combine like terms: 1.277777778 + 0.1111111112 = 1.3888888892
0.1111111112 + 0.6666666667x + x2 = 1.3888888892

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 1.3888888892

Calculate the square root of the right side: 1.178511302

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 1.178511302 and -1.178511302.

Subproblem 1
x + 0.3333333334 = 1.178511302

Simplifying
x + 0.3333333334 = 1.178511302

Reorder the terms:
0.3333333334 + x = 1.178511302

Solving
0.3333333334 + x = 1.178511302

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 1.178511302 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 1.178511302 + -0.3333333334
x = 1.178511302 + -0.3333333334

Combine like terms: 1.178511302 + -0.3333333334 = 0.8451779686
x = 0.8451779686

Simplifying
x = 0.8451779686

Subproblem 2
x + 0.3333333334 = -1.178511302

Simplifying
x + 0.3333333334 = -1.178511302

Reorder the terms:
0.3333333334 + x = -1.178511302

Solving
0.3333333334 + x = -1.178511302

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -1.178511302 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -1.178511302 + -0.3333333334
x = -1.178511302 + -0.3333333334

Combine like terms: -1.178511302 + -0.3333333334 = -1.5118446354
x = -1.5118446354

Simplifying
x = -1.5118446354

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.8451779686, -1.5118446354}
Solution
x = {0.8451779686, -1.5118446354}