13x^2+12x+2=0

Solution for 13x^2+12x+2=0 equation:

Simplifying
13x2 + 12x + 2 = 0

Reorder the terms:
2 + 12x + 13x2 = 0

Solving
2 + 12x + 13x2 = 0

Solving for variable 'x'.

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

Divide each side by '13'.
0.1538461538 + 0.9230769231x + x2 = 0

Move the constant term to the right:

Add '-0.1538461538' to each side of the equation.
0.1538461538 + 0.9230769231x + -0.1538461538 + x2 = 0 + -0.1538461538

Reorder the terms:
0.1538461538 + -0.1538461538 + 0.9230769231x + x2 = 0 + -0.1538461538

Combine like terms: 0.1538461538 + -0.1538461538 = 0.0000000000
0.0000000000 + 0.9230769231x + x2 = 0 + -0.1538461538
0.9230769231x + x2 = 0 + -0.1538461538

Combine like terms: 0 + -0.1538461538 = -0.1538461538
0.9230769231x + x2 = -0.1538461538

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 = -0.1538461538 + 0.2130177515

Reorder the terms:
0.2130177515 + 0.9230769231x + x2 = -0.1538461538 + 0.2130177515

Combine like terms: -0.1538461538 + 0.2130177515 = 0.0591715977
0.2130177515 + 0.9230769231x + x2 = 0.0591715977

Factor a perfect square on the left side:
(x + 0.4615384616)(x + 0.4615384616) = 0.0591715977

Calculate the square root of the right side: 0.243252128

Break this problem into two subproblems by setting 
(x + 0.4615384616) equal to 0.243252128 and -0.243252128.

Subproblem 1
x + 0.4615384616 = 0.243252128

Simplifying
x + 0.4615384616 = 0.243252128

Reorder the terms:
0.4615384616 + x = 0.243252128

Solving
0.4615384616 + x = 0.243252128

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 = 0.243252128 + -0.4615384616

Combine like terms: 0.4615384616 + -0.4615384616 = 0.0000000000
0.0000000000 + x = 0.243252128 + -0.4615384616
x = 0.243252128 + -0.4615384616

Combine like terms: 0.243252128 + -0.4615384616 = -0.2182863336
x = -0.2182863336

Simplifying
x = -0.2182863336

Subproblem 2
x + 0.4615384616 = -0.243252128

Simplifying
x + 0.4615384616 = -0.243252128

Reorder the terms:
0.4615384616 + x = -0.243252128

Solving
0.4615384616 + x = -0.243252128

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 = -0.243252128 + -0.4615384616

Combine like terms: 0.4615384616 + -0.4615384616 = 0.0000000000
0.0000000000 + x = -0.243252128 + -0.4615384616
x = -0.243252128 + -0.4615384616

Combine like terms: -0.243252128 + -0.4615384616 = -0.7047905896
x = -0.7047905896

Simplifying
x = -0.7047905896

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.2182863336, -0.7047905896}