0=9x^2+24x+11

Solution for 0=9x^2+24x+11 equation:

Simplifying
0 = 9x2 + 24x + 11

Reorder the terms:
0 = 11 + 24x + 9x2

Solving
0 = 11 + 24x + 9x2

Solving for variable 'x'.

Combine like terms: 0 + -11 = -11
-11 + -24x + -9x2 = 11 + 24x + 9x2 + -11 + -24x + -9x2

Reorder the terms:
-11 + -24x + -9x2 = 11 + -11 + 24x + -24x + 9x2 + -9x2

Combine like terms: 11 + -11 = 0
-11 + -24x + -9x2 = 0 + 24x + -24x + 9x2 + -9x2
-11 + -24x + -9x2 = 24x + -24x + 9x2 + -9x2

Combine like terms: 24x + -24x = 0
-11 + -24x + -9x2 = 0 + 9x2 + -9x2
-11 + -24x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
-11 + -24x + -9x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(11 + 24x + 9x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(11 + 24x + 9x2)' equal to zero and attempt to solve:

Simplifying
11 + 24x + 9x2 = 0

Solving
11 + 24x + 9x2 = 0

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

Divide each side by '9'.
1.222222222 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '-1.222222222' to each side of the equation.
1.222222222 + 2.666666667x + -1.222222222 + x2 = 0 + -1.222222222

Reorder the terms:
1.222222222 + -1.222222222 + 2.666666667x + x2 = 0 + -1.222222222

Combine like terms: 1.222222222 + -1.222222222 = 0.000000000
0.000000000 + 2.666666667x + x2 = 0 + -1.222222222
2.666666667x + x2 = 0 + -1.222222222

Combine like terms: 0 + -1.222222222 = -1.222222222
2.666666667x + x2 = -1.222222222

The x term is 2.666666667x.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667x + 1.777777780 + x2 = -1.222222222 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = -1.222222222 + 1.777777780

Combine like terms: -1.222222222 + 1.777777780 = 0.555555558
1.777777780 + 2.666666667x + x2 = 0.555555558

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = 0.555555558

Calculate the square root of the right side: 0.745355994

Break this problem into two subproblems by setting 
(x + 1.333333334) equal to 0.745355994 and -0.745355994.

Subproblem 1
x + 1.333333334 = 0.745355994

Simplifying
x + 1.333333334 = 0.745355994

Reorder the terms:
1.333333334 + x = 0.745355994

Solving
1.333333334 + x = 0.745355994

Solving for variable 'x'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + x = 0.745355994 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + x = 0.745355994 + -1.333333334
x = 0.745355994 + -1.333333334

Combine like terms: 0.745355994 + -1.333333334 = -0.58797734
x = -0.58797734

Simplifying
x = -0.58797734

Subproblem 2
x + 1.333333334 = -0.745355994

Simplifying
x + 1.333333334 = -0.745355994

Reorder the terms:
1.333333334 + x = -0.745355994

Solving
1.333333334 + x = -0.745355994

Solving for variable 'x'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + x = -0.745355994 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + x = -0.745355994 + -1.333333334
x = -0.745355994 + -1.333333334

Combine like terms: -0.745355994 + -1.333333334 = -2.078689328
x = -2.078689328

Simplifying
x = -2.078689328

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.58797734, -2.078689328}
Solution
x = {-0.58797734, -2.078689328}