6+2(x+8)3x+11+x=

Solution for 6+2(x+8)3x+11+x= equation:

Simplifying
6 + 2(x + 8) * 3x + 11 + x = 0

Reorder the terms:
6 + 2(8 + x) * 3x + 11 + x = 0

Reorder the terms for easier multiplication:
6 + 2 * 3x(8 + x) + 11 + x = 0

Multiply 2 * 3
6 + 6x(8 + x) + 11 + x = 0
6 + (8 * 6x + x * 6x) + 11 + x = 0
6 + (48x + 6x2) + 11 + x = 0

Reorder the terms:
6 + 11 + 48x + x + 6x2 = 0

Combine like terms: 6 + 11 = 17
17 + 48x + x + 6x2 = 0

Combine like terms: 48x + x = 49x
17 + 49x + 6x2 = 0

Solving
17 + 49x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
2.833333333 + 8.166666667x + x2 = 0

Move the constant term to the right:

Add '-2.833333333' to each side of the equation.
2.833333333 + 8.166666667x + -2.833333333 + x2 = 0 + -2.833333333

Reorder the terms:
2.833333333 + -2.833333333 + 8.166666667x + x2 = 0 + -2.833333333

Combine like terms: 2.833333333 + -2.833333333 = 0.000000000
0.000000000 + 8.166666667x + x2 = 0 + -2.833333333
8.166666667x + x2 = 0 + -2.833333333

Combine like terms: 0 + -2.833333333 = -2.833333333
8.166666667x + x2 = -2.833333333

The x term is 8.166666667x.  Take half its coefficient (4.083333334).
Square it (16.67361112) and add it to both sides.

Add '16.67361112' to each side of the equation.
8.166666667x + 16.67361112 + x2 = -2.833333333 + 16.67361112

Reorder the terms:
16.67361112 + 8.166666667x + x2 = -2.833333333 + 16.67361112

Combine like terms: -2.833333333 + 16.67361112 = 13.840277787
16.67361112 + 8.166666667x + x2 = 13.840277787

Factor a perfect square on the left side:
(x + 4.083333334)(x + 4.083333334) = 13.840277787

Calculate the square root of the right side: 3.720252382

Break this problem into two subproblems by setting 
(x + 4.083333334) equal to 3.720252382 and -3.720252382.

Subproblem 1
x + 4.083333334 = 3.720252382

Simplifying
x + 4.083333334 = 3.720252382

Reorder the terms:
4.083333334 + x = 3.720252382

Solving
4.083333334 + x = 3.720252382

Solving for variable 'x'.

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

Add '-4.083333334' to each side of the equation.
4.083333334 + -4.083333334 + x = 3.720252382 + -4.083333334

Combine like terms: 4.083333334 + -4.083333334 = 0.000000000
0.000000000 + x = 3.720252382 + -4.083333334
x = 3.720252382 + -4.083333334

Combine like terms: 3.720252382 + -4.083333334 = -0.363080952
x = -0.363080952

Simplifying
x = -0.363080952

Subproblem 2
x + 4.083333334 = -3.720252382

Simplifying
x + 4.083333334 = -3.720252382

Reorder the terms:
4.083333334 + x = -3.720252382

Solving
4.083333334 + x = -3.720252382

Solving for variable 'x'.

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

Add '-4.083333334' to each side of the equation.
4.083333334 + -4.083333334 + x = -3.720252382 + -4.083333334

Combine like terms: 4.083333334 + -4.083333334 = 0.000000000
0.000000000 + x = -3.720252382 + -4.083333334
x = -3.720252382 + -4.083333334

Combine like terms: -3.720252382 + -4.083333334 = -7.803585716
x = -7.803585716

Simplifying
x = -7.803585716

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.363080952, -7.803585716}