x^2+13*x-72=0

Solution for x^2+13*x-72=0 equation:

Simplifying
x2 + 13x + -72 = 0

Reorder the terms:
-72 + 13x + x2 = 0

Solving
-72 + 13x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '72' to each side of the equation.
-72 + 13x + 72 + x2 = 0 + 72

Reorder the terms:
-72 + 72 + 13x + x2 = 0 + 72

Combine like terms: -72 + 72 = 0
0 + 13x + x2 = 0 + 72
13x + x2 = 0 + 72

Combine like terms: 0 + 72 = 72
13x + x2 = 72

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 = 72 + 42.25

Reorder the terms:
42.25 + 13x + x2 = 72 + 42.25

Combine like terms: 72 + 42.25 = 114.25
42.25 + 13x + x2 = 114.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 114.25

Calculate the square root of the right side: 10.688779163

Break this problem into two subproblems by setting 
(x + 6.5) equal to 10.688779163 and -10.688779163.

Subproblem 1
x + 6.5 = 10.688779163

Simplifying
x + 6.5 = 10.688779163

Reorder the terms:
6.5 + x = 10.688779163

Solving
6.5 + x = 10.688779163

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 = 10.688779163 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = 10.688779163 + -6.5
x = 10.688779163 + -6.5

Combine like terms: 10.688779163 + -6.5 = 4.188779163
x = 4.188779163

Simplifying
x = 4.188779163

Subproblem 2
x + 6.5 = -10.688779163

Simplifying
x + 6.5 = -10.688779163

Reorder the terms:
6.5 + x = -10.688779163

Solving
6.5 + x = -10.688779163

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 = -10.688779163 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = -10.688779163 + -6.5
x = -10.688779163 + -6.5

Combine like terms: -10.688779163 + -6.5 = -17.188779163
x = -17.188779163

Simplifying
x = -17.188779163

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.188779163, -17.188779163}