(2x+11)(x-5)=72

Solution for (2x+11)(x-5)=72 equation:

Simplifying
(2x + 11)(x + -5) = 72

Reorder the terms:
(11 + 2x)(x + -5) = 72

Reorder the terms:
(11 + 2x)(-5 + x) = 72

Multiply (11 + 2x) * (-5 + x)
(11(-5 + x) + 2x * (-5 + x)) = 72
((-5 * 11 + x * 11) + 2x * (-5 + x)) = 72
((-55 + 11x) + 2x * (-5 + x)) = 72
(-55 + 11x + (-5 * 2x + x * 2x)) = 72
(-55 + 11x + (-10x + 2x2)) = 72

Combine like terms: 11x + -10x = 1x
(-55 + 1x + 2x2) = 72

Solving
-55 + 1x + 2x2 = 72

Solving for variable 'x'.

Reorder the terms:
-55 + -72 + 1x + 2x2 = 72 + -72

Combine like terms: -55 + -72 = -127
-127 + 1x + 2x2 = 72 + -72

Combine like terms: 72 + -72 = 0
-127 + 1x + 2x2 = 0

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

Divide each side by '2'.
-63.5 + 0.5x + x2 = 0

Move the constant term to the right:

Add '63.5' to each side of the equation.
-63.5 + 0.5x + 63.5 + x2 = 0 + 63.5

Reorder the terms:
-63.5 + 63.5 + 0.5x + x2 = 0 + 63.5

Combine like terms: -63.5 + 63.5 = 0.0
0.0 + 0.5x + x2 = 0 + 63.5
0.5x + x2 = 0 + 63.5

Combine like terms: 0 + 63.5 = 63.5
0.5x + x2 = 63.5

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 = 63.5 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 63.5 + 0.0625

Combine like terms: 63.5 + 0.0625 = 63.5625
0.0625 + 0.5x + x2 = 63.5625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 63.5625

Calculate the square root of the right side: 7.97260936

Break this problem into two subproblems by setting 
(x + 0.25) equal to 7.97260936 and -7.97260936.

Subproblem 1
x + 0.25 = 7.97260936

Simplifying
x + 0.25 = 7.97260936

Reorder the terms:
0.25 + x = 7.97260936

Solving
0.25 + x = 7.97260936

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 = 7.97260936 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 7.97260936 + -0.25
x = 7.97260936 + -0.25

Combine like terms: 7.97260936 + -0.25 = 7.72260936
x = 7.72260936

Simplifying
x = 7.72260936

Subproblem 2
x + 0.25 = -7.97260936

Simplifying
x + 0.25 = -7.97260936

Reorder the terms:
0.25 + x = -7.97260936

Solving
0.25 + x = -7.97260936

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 = -7.97260936 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -7.97260936 + -0.25
x = -7.97260936 + -0.25

Combine like terms: -7.97260936 + -0.25 = -8.22260936
x = -8.22260936

Simplifying
x = -8.22260936

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.72260936, -8.22260936}