2(x+11)(x-5)=100

Solution for 2(x+11)(x-5)=100 equation:

Simplifying
2(x + 11)(x + -5) = 100

Reorder the terms:
2(11 + x)(x + -5) = 100

Reorder the terms:
2(11 + x)(-5 + x) = 100

Multiply (11 + x) * (-5 + x)
2(11(-5 + x) + x(-5 + x)) = 100
2((-5 * 11 + x * 11) + x(-5 + x)) = 100
2((-55 + 11x) + x(-5 + x)) = 100
2(-55 + 11x + (-5 * x + x * x)) = 100
2(-55 + 11x + (-5x + x2)) = 100

Combine like terms: 11x + -5x = 6x
2(-55 + 6x + x2) = 100
(-55 * 2 + 6x * 2 + x2 * 2) = 100
(-110 + 12x + 2x2) = 100

Solving
-110 + 12x + 2x2 = 100

Solving for variable 'x'.

Reorder the terms:
-110 + -100 + 12x + 2x2 = 100 + -100

Combine like terms: -110 + -100 = -210
-210 + 12x + 2x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-210 + 12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-105 + 6x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-105 + 6x + x2)' equal to zero and attempt to solve:

Simplifying
-105 + 6x + x2 = 0

Solving
-105 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '105' to each side of the equation.
-105 + 6x + 105 + x2 = 0 + 105

Reorder the terms:
-105 + 105 + 6x + x2 = 0 + 105

Combine like terms: -105 + 105 = 0
0 + 6x + x2 = 0 + 105
6x + x2 = 0 + 105

Combine like terms: 0 + 105 = 105
6x + x2 = 105

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 = 105 + 9

Reorder the terms:
9 + 6x + x2 = 105 + 9

Combine like terms: 105 + 9 = 114
9 + 6x + x2 = 114

Factor a perfect square on the left side:
(x + 3)(x + 3) = 114

Calculate the square root of the right side: 10.677078252

Break this problem into two subproblems by setting 
(x + 3) equal to 10.677078252 and -10.677078252.

Subproblem 1
x + 3 = 10.677078252

Simplifying
x + 3 = 10.677078252

Reorder the terms:
3 + x = 10.677078252

Solving
3 + x = 10.677078252

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 = 10.677078252 + -3

Combine like terms: 3 + -3 = 0
0 + x = 10.677078252 + -3
x = 10.677078252 + -3

Combine like terms: 10.677078252 + -3 = 7.677078252
x = 7.677078252

Simplifying
x = 7.677078252

Subproblem 2
x + 3 = -10.677078252

Simplifying
x + 3 = -10.677078252

Reorder the terms:
3 + x = -10.677078252

Solving
3 + x = -10.677078252

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 = -10.677078252 + -3

Combine like terms: 3 + -3 = 0
0 + x = -10.677078252 + -3
x = -10.677078252 + -3

Combine like terms: -10.677078252 + -3 = -13.677078252
x = -13.677078252

Simplifying
x = -13.677078252

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.677078252, -13.677078252}
Solution
x = {7.677078252, -13.677078252}