11x(4x-11)=6+6x

Solution for 11x(4x-11)=6+6x equation:

Simplifying
11x(4x + -11) = 6 + 6x

Reorder the terms:
11x(-11 + 4x) = 6 + 6x
(-11 * 11x + 4x * 11x) = 6 + 6x
(-121x + 44x2) = 6 + 6x

Solving
-121x + 44x2 = 6 + 6x

Solving for variable 'x'.

Reorder the terms:
-6 + -121x + -6x + 44x2 = 6 + 6x + -6 + -6x

Combine like terms: -121x + -6x = -127x
-6 + -127x + 44x2 = 6 + 6x + -6 + -6x

Reorder the terms:
-6 + -127x + 44x2 = 6 + -6 + 6x + -6x

Combine like terms: 6 + -6 = 0
-6 + -127x + 44x2 = 0 + 6x + -6x
-6 + -127x + 44x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-6 + -127x + 44x2 = 0

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

Divide each side by '44'.
-0.1363636364 + -2.886363636x + x2 = 0

Move the constant term to the right:

Add '0.1363636364' to each side of the equation.
-0.1363636364 + -2.886363636x + 0.1363636364 + x2 = 0 + 0.1363636364

Reorder the terms:
-0.1363636364 + 0.1363636364 + -2.886363636x + x2 = 0 + 0.1363636364

Combine like terms: -0.1363636364 + 0.1363636364 = 0.0000000000
0.0000000000 + -2.886363636x + x2 = 0 + 0.1363636364
-2.886363636x + x2 = 0 + 0.1363636364

Combine like terms: 0 + 0.1363636364 = 0.1363636364
-2.886363636x + x2 = 0.1363636364

The x term is -2.886363636x.  Take half its coefficient (-1.443181818).
Square it (2.082773760) and add it to both sides.

Add '2.082773760' to each side of the equation.
-2.886363636x + 2.082773760 + x2 = 0.1363636364 + 2.082773760

Reorder the terms:
2.082773760 + -2.886363636x + x2 = 0.1363636364 + 2.082773760

Combine like terms: 0.1363636364 + 2.082773760 = 2.2191373964
2.082773760 + -2.886363636x + x2 = 2.2191373964

Factor a perfect square on the left side:
(x + -1.443181818)(x + -1.443181818) = 2.2191373964

Calculate the square root of the right side: 1.489676944

Break this problem into two subproblems by setting 
(x + -1.443181818) equal to 1.489676944 and -1.489676944.

Subproblem 1
x + -1.443181818 = 1.489676944

Simplifying
x + -1.443181818 = 1.489676944

Reorder the terms:
-1.443181818 + x = 1.489676944

Solving
-1.443181818 + x = 1.489676944

Solving for variable 'x'.

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

Add '1.443181818' to each side of the equation.
-1.443181818 + 1.443181818 + x = 1.489676944 + 1.443181818

Combine like terms: -1.443181818 + 1.443181818 = 0.000000000
0.000000000 + x = 1.489676944 + 1.443181818
x = 1.489676944 + 1.443181818

Combine like terms: 1.489676944 + 1.443181818 = 2.932858762
x = 2.932858762

Simplifying
x = 2.932858762

Subproblem 2
x + -1.443181818 = -1.489676944

Simplifying
x + -1.443181818 = -1.489676944

Reorder the terms:
-1.443181818 + x = -1.489676944

Solving
-1.443181818 + x = -1.489676944

Solving for variable 'x'.

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

Add '1.443181818' to each side of the equation.
-1.443181818 + 1.443181818 + x = -1.489676944 + 1.443181818

Combine like terms: -1.443181818 + 1.443181818 = 0.000000000
0.000000000 + x = -1.489676944 + 1.443181818
x = -1.489676944 + 1.443181818

Combine like terms: -1.489676944 + 1.443181818 = -0.046495126
x = -0.046495126

Simplifying
x = -0.046495126

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.932858762, -0.046495126}