2(x+11)(2+x)=198

Solution for 2(x+11)(2+x)=198 equation:

Simplifying
2(x + 11)(2 + x) = 198

Reorder the terms:
2(11 + x)(2 + x) = 198

Multiply (11 + x) * (2 + x)
2(11(2 + x) + x(2 + x)) = 198
2((2 * 11 + x * 11) + x(2 + x)) = 198
2((22 + 11x) + x(2 + x)) = 198
2(22 + 11x + (2 * x + x * x)) = 198
2(22 + 11x + (2x + x2)) = 198

Combine like terms: 11x + 2x = 13x
2(22 + 13x + x2) = 198
(22 * 2 + 13x * 2 + x2 * 2) = 198
(44 + 26x + 2x2) = 198

Solving
44 + 26x + 2x2 = 198

Solving for variable 'x'.

Reorder the terms:
44 + -198 + 26x + 2x2 = 198 + -198

Combine like terms: 44 + -198 = -154
-154 + 26x + 2x2 = 198 + -198

Combine like terms: 198 + -198 = 0
-154 + 26x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-77 + 13x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-77 + 13x + x2)' equal to zero and attempt to solve:

Simplifying
-77 + 13x + x2 = 0

Solving
-77 + 13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '77' to each side of the equation.
-77 + 13x + 77 + x2 = 0 + 77

Reorder the terms:
-77 + 77 + 13x + x2 = 0 + 77

Combine like terms: -77 + 77 = 0
0 + 13x + x2 = 0 + 77
13x + x2 = 0 + 77

Combine like terms: 0 + 77 = 77
13x + x2 = 77

The x term is 13x.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13x + 42.25 + x2 = 77 + 42.25

Reorder the terms:
42.25 + 13x + x2 = 77 + 42.25

Combine like terms: 77 + 42.25 = 119.25
42.25 + 13x + x2 = 119.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 119.25

Calculate the square root of the right side: 10.920164834

Break this problem into two subproblems by setting 
(x + 6.5) equal to 10.920164834 and -10.920164834.

Subproblem 1
x + 6.5 = 10.920164834

Simplifying
x + 6.5 = 10.920164834

Reorder the terms:
6.5 + x = 10.920164834

Solving
6.5 + x = 10.920164834

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = 10.920164834 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = 10.920164834 + -6.5
x = 10.920164834 + -6.5

Combine like terms: 10.920164834 + -6.5 = 4.420164834
x = 4.420164834

Simplifying
x = 4.420164834

Subproblem 2
x + 6.5 = -10.920164834

Simplifying
x + 6.5 = -10.920164834

Reorder the terms:
6.5 + x = -10.920164834

Solving
6.5 + x = -10.920164834

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = -10.920164834 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = -10.920164834 + -6.5
x = -10.920164834 + -6.5

Combine like terms: -10.920164834 + -6.5 = -17.420164834
x = -17.420164834

Simplifying
x = -17.420164834

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.420164834, -17.420164834}
Solution
x = {4.420164834, -17.420164834}