m^2+69m-680=0

Solution for m^2+69m-680=0 equation:

Simplifying
m2 + 69m + -680 = 0

Reorder the terms:
-680 + 69m + m2 = 0

Solving
-680 + 69m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '680' to each side of the equation.
-680 + 69m + 680 + m2 = 0 + 680

Reorder the terms:
-680 + 680 + 69m + m2 = 0 + 680

Combine like terms: -680 + 680 = 0
0 + 69m + m2 = 0 + 680
69m + m2 = 0 + 680

Combine like terms: 0 + 680 = 680
69m + m2 = 680

The m term is 69m.  Take half its coefficient (34.5).
Square it (1190.25) and add it to both sides.

Add '1190.25' to each side of the equation.
69m + 1190.25 + m2 = 680 + 1190.25

Reorder the terms:
1190.25 + 69m + m2 = 680 + 1190.25

Combine like terms: 680 + 1190.25 = 1870.25
1190.25 + 69m + m2 = 1870.25

Factor a perfect square on the left side:
(m + 34.5)(m + 34.5) = 1870.25

Calculate the square root of the right side: 43.246387132

Break this problem into two subproblems by setting 
(m + 34.5) equal to 43.246387132 and -43.246387132.

Subproblem 1
m + 34.5 = 43.246387132

Simplifying
m + 34.5 = 43.246387132

Reorder the terms:
34.5 + m = 43.246387132

Solving
34.5 + m = 43.246387132

Solving for variable 'm'.

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

Add '-34.5' to each side of the equation.
34.5 + -34.5 + m = 43.246387132 + -34.5

Combine like terms: 34.5 + -34.5 = 0.0
0.0 + m = 43.246387132 + -34.5
m = 43.246387132 + -34.5

Combine like terms: 43.246387132 + -34.5 = 8.746387132
m = 8.746387132

Simplifying
m = 8.746387132

Subproblem 2
m + 34.5 = -43.246387132

Simplifying
m + 34.5 = -43.246387132

Reorder the terms:
34.5 + m = -43.246387132

Solving
34.5 + m = -43.246387132

Solving for variable 'm'.

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

Add '-34.5' to each side of the equation.
34.5 + -34.5 + m = -43.246387132 + -34.5

Combine like terms: 34.5 + -34.5 = 0.0
0.0 + m = -43.246387132 + -34.5
m = -43.246387132 + -34.5

Combine like terms: -43.246387132 + -34.5 = -77.746387132
m = -77.746387132

Simplifying
m = -77.746387132

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {8.746387132, -77.746387132}