(x-5)(2x+11)=130

Solution for (x-5)(2x+11)=130 equation:

Simplifying
(x + -5)(2x + 11) = 130

Reorder the terms:
(-5 + x)(2x + 11) = 130

Reorder the terms:
(-5 + x)(11 + 2x) = 130

Multiply (-5 + x) * (11 + 2x)
(-5(11 + 2x) + x(11 + 2x)) = 130
((11 * -5 + 2x * -5) + x(11 + 2x)) = 130
((-55 + -10x) + x(11 + 2x)) = 130
(-55 + -10x + (11 * x + 2x * x)) = 130
(-55 + -10x + (11x + 2x2)) = 130

Combine like terms: -10x + 11x = 1x
(-55 + 1x + 2x2) = 130

Solving
-55 + 1x + 2x2 = 130

Solving for variable 'x'.

Reorder the terms:
-55 + -130 + 1x + 2x2 = 130 + -130

Combine like terms: -55 + -130 = -185
-185 + 1x + 2x2 = 130 + -130

Combine like terms: 130 + -130 = 0
-185 + 1x + 2x2 = 0

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

Divide each side by '2'.
-92.5 + 0.5x + x2 = 0

Move the constant term to the right:

Add '92.5' to each side of the equation.
-92.5 + 0.5x + 92.5 + x2 = 0 + 92.5

Reorder the terms:
-92.5 + 92.5 + 0.5x + x2 = 0 + 92.5

Combine like terms: -92.5 + 92.5 = 0.0
0.0 + 0.5x + x2 = 0 + 92.5
0.5x + x2 = 0 + 92.5

Combine like terms: 0 + 92.5 = 92.5
0.5x + x2 = 92.5

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 92.5 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 92.5 + 0.0625

Combine like terms: 92.5 + 0.0625 = 92.5625
0.0625 + 0.5x + x2 = 92.5625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 92.5625

Calculate the square root of the right side: 9.620940702

Break this problem into two subproblems by setting 
(x + 0.25) equal to 9.620940702 and -9.620940702.

Subproblem 1
x + 0.25 = 9.620940702

Simplifying
x + 0.25 = 9.620940702

Reorder the terms:
0.25 + x = 9.620940702

Solving
0.25 + x = 9.620940702

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 9.620940702 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 9.620940702 + -0.25
x = 9.620940702 + -0.25

Combine like terms: 9.620940702 + -0.25 = 9.370940702
x = 9.370940702

Simplifying
x = 9.370940702

Subproblem 2
x + 0.25 = -9.620940702

Simplifying
x + 0.25 = -9.620940702

Reorder the terms:
0.25 + x = -9.620940702

Solving
0.25 + x = -9.620940702

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -9.620940702 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -9.620940702 + -0.25
x = -9.620940702 + -0.25

Combine like terms: -9.620940702 + -0.25 = -9.870940702
x = -9.870940702

Simplifying
x = -9.870940702

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.370940702, -9.870940702}