72=x^2+11x

Solution for 72=x^2+11x equation:

Simplifying
72 = x2 + 11x

Reorder the terms:
72 = 11x + x2

Solving
72 = 11x + x2

Solving for variable 'x'.

Reorder the terms:
72 + -11x + -1x2 = 11x + -11x + x2 + -1x2

Combine like terms: 11x + -11x = 0
72 + -11x + -1x2 = 0 + x2 + -1x2
72 + -11x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
72 + -11x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-72 + 11x + x2 = 0

Move the constant term to the right:

Add '72' to each side of the equation.
-72 + 11x + 72 + x2 = 0 + 72

Reorder the terms:
-72 + 72 + 11x + x2 = 0 + 72

Combine like terms: -72 + 72 = 0
0 + 11x + x2 = 0 + 72
11x + x2 = 0 + 72

Combine like terms: 0 + 72 = 72
11x + x2 = 72

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = 72 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 72 + 30.25

Combine like terms: 72 + 30.25 = 102.25
30.25 + 11x + x2 = 102.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 102.25

Calculate the square root of the right side: 10.111874208

Break this problem into two subproblems by setting 
(x + 5.5) equal to 10.111874208 and -10.111874208.

Subproblem 1
x + 5.5 = 10.111874208

Simplifying
x + 5.5 = 10.111874208

Reorder the terms:
5.5 + x = 10.111874208

Solving
5.5 + x = 10.111874208

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = 10.111874208 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 10.111874208 + -5.5
x = 10.111874208 + -5.5

Combine like terms: 10.111874208 + -5.5 = 4.611874208
x = 4.611874208

Simplifying
x = 4.611874208

Subproblem 2
x + 5.5 = -10.111874208

Simplifying
x + 5.5 = -10.111874208

Reorder the terms:
5.5 + x = -10.111874208

Solving
5.5 + x = -10.111874208

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = -10.111874208 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -10.111874208 + -5.5
x = -10.111874208 + -5.5

Combine like terms: -10.111874208 + -5.5 = -15.611874208
x = -15.611874208

Simplifying
x = -15.611874208

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.611874208, -15.611874208}