11+7(2x-1)-9x=x(x+11)

Solution for 11+7(2x-1)-9x=x(x+11) equation:

Simplifying
11 + 7(2x + -1) + -9x = x(x + 11)

Reorder the terms:
11 + 7(-1 + 2x) + -9x = x(x + 11)
11 + (-1 * 7 + 2x * 7) + -9x = x(x + 11)
11 + (-7 + 14x) + -9x = x(x + 11)

Combine like terms: 11 + -7 = 4
4 + 14x + -9x = x(x + 11)

Combine like terms: 14x + -9x = 5x
4 + 5x = x(x + 11)

Reorder the terms:
4 + 5x = x(11 + x)
4 + 5x = (11 * x + x * x)
4 + 5x = (11x + x2)

Solving
4 + 5x = 11x + x2

Solving for variable 'x'.

Combine like terms: 5x + -11x = -6x
4 + -6x + -1x2 = 11x + x2 + -11x + -1x2

Reorder the terms:
4 + -6x + -1x2 = 11x + -11x + x2 + -1x2

Combine like terms: 11x + -11x = 0
4 + -6x + -1x2 = 0 + x2 + -1x2
4 + -6x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4 + -6x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-4 + 6x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 6x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 6x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 6x + x2 = 0 + 4
6x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
6x + x2 = 4

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 4 + 9

Reorder the terms:
9 + 6x + x2 = 4 + 9

Combine like terms: 4 + 9 = 13
9 + 6x + x2 = 13

Factor a perfect square on the left side:
(x + 3)(x + 3) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(x + 3) equal to 3.605551275 and -3.605551275.

Subproblem 1
x + 3 = 3.605551275

Simplifying
x + 3 = 3.605551275

Reorder the terms:
3 + x = 3.605551275

Solving
3 + x = 3.605551275

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 3.605551275 + -3

Combine like terms: 3 + -3 = 0
0 + x = 3.605551275 + -3
x = 3.605551275 + -3

Combine like terms: 3.605551275 + -3 = 0.605551275
x = 0.605551275

Simplifying
x = 0.605551275

Subproblem 2
x + 3 = -3.605551275

Simplifying
x + 3 = -3.605551275

Reorder the terms:
3 + x = -3.605551275

Solving
3 + x = -3.605551275

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -3.605551275 + -3

Combine like terms: 3 + -3 = 0
0 + x = -3.605551275 + -3
x = -3.605551275 + -3

Combine like terms: -3.605551275 + -3 = -6.605551275
x = -6.605551275

Simplifying
x = -6.605551275

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.605551275, -6.605551275}