12x^2+24x+11=0

Solution for 12x^2+24x+11=0 equation:

Simplifying
12x2 + 24x + 11 = 0

Reorder the terms:
11 + 24x + 12x2 = 0

Solving
11 + 24x + 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'.
0.9166666667 + 2x + x2 = 0

Move the constant term to the right:

Add '-0.9166666667' to each side of the equation.
0.9166666667 + 2x + -0.9166666667 + x2 = 0 + -0.9166666667

Reorder the terms:
0.9166666667 + -0.9166666667 + 2x + x2 = 0 + -0.9166666667

Combine like terms: 0.9166666667 + -0.9166666667 = 0.0000000000
0.0000000000 + 2x + x2 = 0 + -0.9166666667
2x + x2 = 0 + -0.9166666667

Combine like terms: 0 + -0.9166666667 = -0.9166666667
2x + x2 = -0.9166666667

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -0.9166666667 + 1

Reorder the terms:
1 + 2x + x2 = -0.9166666667 + 1

Combine like terms: -0.9166666667 + 1 = 0.0833333333
1 + 2x + x2 = 0.0833333333

Factor a perfect square on the left side:
(x + 1)(x + 1) = 0.0833333333

Calculate the square root of the right side: 0.288675135

Break this problem into two subproblems by setting 
(x + 1) equal to 0.288675135 and -0.288675135.

Subproblem 1
x + 1 = 0.288675135

Simplifying
x + 1 = 0.288675135

Reorder the terms:
1 + x = 0.288675135

Solving
1 + x = 0.288675135

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 0.288675135 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0.288675135 + -1
x = 0.288675135 + -1

Combine like terms: 0.288675135 + -1 = -0.711324865
x = -0.711324865

Simplifying
x = -0.711324865

Subproblem 2
x + 1 = -0.288675135

Simplifying
x + 1 = -0.288675135

Reorder the terms:
1 + x = -0.288675135

Solving
1 + x = -0.288675135

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -0.288675135 + -1

Combine like terms: 1 + -1 = 0
0 + x = -0.288675135 + -1
x = -0.288675135 + -1

Combine like terms: -0.288675135 + -1 = -1.288675135
x = -1.288675135

Simplifying
x = -1.288675135

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.711324865, -1.288675135}