m^2-2m-72=0

Solution for m^2-2m-72=0 equation:

Simplifying
m2 + -2m + -72 = 0

Reorder the terms:
-72 + -2m + m2 = 0

Solving
-72 + -2m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '72' to each side of the equation.
-72 + -2m + 72 + m2 = 0 + 72

Reorder the terms:
-72 + 72 + -2m + m2 = 0 + 72

Combine like terms: -72 + 72 = 0
0 + -2m + m2 = 0 + 72
-2m + m2 = 0 + 72

Combine like terms: 0 + 72 = 72
-2m + m2 = 72

The m term is -2m.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2m + 1 + m2 = 72 + 1

Reorder the terms:
1 + -2m + m2 = 72 + 1

Combine like terms: 72 + 1 = 73
1 + -2m + m2 = 73

Factor a perfect square on the left side:
(m + -1)(m + -1) = 73

Calculate the square root of the right side: 8.544003745

Break this problem into two subproblems by setting 
(m + -1) equal to 8.544003745 and -8.544003745.

Subproblem 1
m + -1 = 8.544003745

Simplifying
m + -1 = 8.544003745

Reorder the terms:
-1 + m = 8.544003745

Solving
-1 + m = 8.544003745

Solving for variable 'm'.

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

Add '1' to each side of the equation.
-1 + 1 + m = 8.544003745 + 1

Combine like terms: -1 + 1 = 0
0 + m = 8.544003745 + 1
m = 8.544003745 + 1

Combine like terms: 8.544003745 + 1 = 9.544003745
m = 9.544003745

Simplifying
m = 9.544003745

Subproblem 2
m + -1 = -8.544003745

Simplifying
m + -1 = -8.544003745

Reorder the terms:
-1 + m = -8.544003745

Solving
-1 + m = -8.544003745

Solving for variable 'm'.

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

Add '1' to each side of the equation.
-1 + 1 + m = -8.544003745 + 1

Combine like terms: -1 + 1 = 0
0 + m = -8.544003745 + 1
m = -8.544003745 + 1

Combine like terms: -8.544003745 + 1 = -7.544003745
m = -7.544003745

Simplifying
m = -7.544003745

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {9.544003745, -7.544003745}