x^2+25x-72=0

Solution for x^2+25x-72=0 equation:

Simplifying
x2 + 25x + -72 = 0

Reorder the terms:
-72 + 25x + x2 = 0

Solving
-72 + 25x + 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 + 25x + 72 + x2 = 0 + 72

Reorder the terms:
-72 + 72 + 25x + x2 = 0 + 72

Combine like terms: -72 + 72 = 0
0 + 25x + x2 = 0 + 72
25x + x2 = 0 + 72

Combine like terms: 0 + 72 = 72
25x + x2 = 72

The x term is 25x.  Take half its coefficient (12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
25x + 156.25 + x2 = 72 + 156.25

Reorder the terms:
156.25 + 25x + x2 = 72 + 156.25

Combine like terms: 72 + 156.25 = 228.25
156.25 + 25x + x2 = 228.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 228.25

Calculate the square root of the right side: 15.10794493

Break this problem into two subproblems by setting 
(x + 12.5) equal to 15.10794493 and -15.10794493.

Subproblem 1
x + 12.5 = 15.10794493

Simplifying
x + 12.5 = 15.10794493

Reorder the terms:
12.5 + x = 15.10794493

Solving
12.5 + x = 15.10794493

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = 15.10794493 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = 15.10794493 + -12.5
x = 15.10794493 + -12.5

Combine like terms: 15.10794493 + -12.5 = 2.60794493
x = 2.60794493

Simplifying
x = 2.60794493

Subproblem 2
x + 12.5 = -15.10794493

Simplifying
x + 12.5 = -15.10794493

Reorder the terms:
12.5 + x = -15.10794493

Solving
12.5 + x = -15.10794493

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = -15.10794493 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = -15.10794493 + -12.5
x = -15.10794493 + -12.5

Combine like terms: -15.10794493 + -12.5 = -27.60794493
x = -27.60794493

Simplifying
x = -27.60794493

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.60794493, -27.60794493}