9x^2+11=24x

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

Simplifying
9x2 + 11 = 24x

Reorder the terms:
11 + 9x2 = 24x

Solving
11 + 9x2 = 24x

Solving for variable 'x'.

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

Combine like terms: 24x + -24x = 0
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 = 2.078689328
x = 2.078689328

Simplifying
x = 2.078689328

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 = 0.58797734
x = 0.58797734

Simplifying
x = 0.58797734

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