12x^2+37x+6=0

Solution for 12x^2+37x+6=0 equation:

Simplifying
12x2 + 37x + 6 = 0

Reorder the terms:
6 + 37x + 12x2 = 0

Solving
6 + 37x + 12x2 = 0

Solving for variable 'x'.

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

Divide each side by '12'.
0.5 + 3.083333333x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 3.083333333x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 3.083333333x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 3.083333333x + x2 = 0 + -0.5
3.083333333x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
3.083333333x + x2 = -0.5

The x term is 3.083333333x.  Take half its coefficient (1.541666667).
Square it (2.376736112) and add it to both sides.

Add '2.376736112' to each side of the equation.
3.083333333x + 2.376736112 + x2 = -0.5 + 2.376736112

Reorder the terms:
2.376736112 + 3.083333333x + x2 = -0.5 + 2.376736112

Combine like terms: -0.5 + 2.376736112 = 1.876736112
2.376736112 + 3.083333333x + x2 = 1.876736112

Factor a perfect square on the left side:
(x + 1.541666667)(x + 1.541666667) = 1.876736112

Calculate the square root of the right side: 1.369940186

Break this problem into two subproblems by setting 
(x + 1.541666667) equal to 1.369940186 and -1.369940186.

Subproblem 1
x + 1.541666667 = 1.369940186

Simplifying
x + 1.541666667 = 1.369940186

Reorder the terms:
1.541666667 + x = 1.369940186

Solving
1.541666667 + x = 1.369940186

Solving for variable 'x'.

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

Add '-1.541666667' to each side of the equation.
1.541666667 + -1.541666667 + x = 1.369940186 + -1.541666667

Combine like terms: 1.541666667 + -1.541666667 = 0.000000000
0.000000000 + x = 1.369940186 + -1.541666667
x = 1.369940186 + -1.541666667

Combine like terms: 1.369940186 + -1.541666667 = -0.171726481
x = -0.171726481

Simplifying
x = -0.171726481

Subproblem 2
x + 1.541666667 = -1.369940186

Simplifying
x + 1.541666667 = -1.369940186

Reorder the terms:
1.541666667 + x = -1.369940186

Solving
1.541666667 + x = -1.369940186

Solving for variable 'x'.

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

Add '-1.541666667' to each side of the equation.
1.541666667 + -1.541666667 + x = -1.369940186 + -1.541666667

Combine like terms: 1.541666667 + -1.541666667 = 0.000000000
0.000000000 + x = -1.369940186 + -1.541666667
x = -1.369940186 + -1.541666667

Combine like terms: -1.369940186 + -1.541666667 = -2.911606853
x = -2.911606853

Simplifying
x = -2.911606853

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.171726481, -2.911606853}