11x^2+12x=6

Solution for 11x^2+12x=6 equation:

Simplifying
11x2 + 12x = 6

Reorder the terms:
12x + 11x2 = 6

Solving
12x + 11x2 = 6

Solving for variable 'x'.

Reorder the terms:
-6 + 12x + 11x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 12x + 11x2 = 0

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

Divide each side by '11'.
-0.5454545455 + 1.090909091x + x2 = 0

Move the constant term to the right:

Add '0.5454545455' to each side of the equation.
-0.5454545455 + 1.090909091x + 0.5454545455 + x2 = 0 + 0.5454545455

Reorder the terms:
-0.5454545455 + 0.5454545455 + 1.090909091x + x2 = 0 + 0.5454545455

Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000
0.0000000000 + 1.090909091x + x2 = 0 + 0.5454545455
1.090909091x + x2 = 0 + 0.5454545455

Combine like terms: 0 + 0.5454545455 = 0.5454545455
1.090909091x + x2 = 0.5454545455

The x term is 1.090909091x.  Take half its coefficient (0.5454545455).
Square it (0.2975206612) and add it to both sides.

Add '0.2975206612' to each side of the equation.
1.090909091x + 0.2975206612 + x2 = 0.5454545455 + 0.2975206612

Reorder the terms:
0.2975206612 + 1.090909091x + x2 = 0.5454545455 + 0.2975206612

Combine like terms: 0.5454545455 + 0.2975206612 = 0.8429752067
0.2975206612 + 1.090909091x + x2 = 0.8429752067

Factor a perfect square on the left side:
(x + 0.5454545455)(x + 0.5454545455) = 0.8429752067

Calculate the square root of the right side: 0.918136813

Break this problem into two subproblems by setting 
(x + 0.5454545455) equal to 0.918136813 and -0.918136813.

Subproblem 1
x + 0.5454545455 = 0.918136813

Simplifying
x + 0.5454545455 = 0.918136813

Reorder the terms:
0.5454545455 + x = 0.918136813

Solving
0.5454545455 + x = 0.918136813

Solving for variable 'x'.

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

Add '-0.5454545455' to each side of the equation.
0.5454545455 + -0.5454545455 + x = 0.918136813 + -0.5454545455

Combine like terms: 0.5454545455 + -0.5454545455 = 0.0000000000
0.0000000000 + x = 0.918136813 + -0.5454545455
x = 0.918136813 + -0.5454545455

Combine like terms: 0.918136813 + -0.5454545455 = 0.3726822675
x = 0.3726822675

Simplifying
x = 0.3726822675

Subproblem 2
x + 0.5454545455 = -0.918136813

Simplifying
x + 0.5454545455 = -0.918136813

Reorder the terms:
0.5454545455 + x = -0.918136813

Solving
0.5454545455 + x = -0.918136813

Solving for variable 'x'.

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

Add '-0.5454545455' to each side of the equation.
0.5454545455 + -0.5454545455 + x = -0.918136813 + -0.5454545455

Combine like terms: 0.5454545455 + -0.5454545455 = 0.0000000000
0.0000000000 + x = -0.918136813 + -0.5454545455
x = -0.918136813 + -0.5454545455

Combine like terms: -0.918136813 + -0.5454545455 = -1.4635913585
x = -1.4635913585

Simplifying
x = -1.4635913585

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.3726822675, -1.4635913585}