m^2+6m-5=0

Solution for m^2+6m-5=0 equation:

Simplifying
m2 + 6m + -5 = 0

Reorder the terms:
-5 + 6m + m2 = 0

Solving
-5 + 6m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 6m + 5 + m2 = 0 + 5

Reorder the terms:
-5 + 5 + 6m + m2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 6m + m2 = 0 + 5
6m + m2 = 0 + 5

Combine like terms: 0 + 5 = 5
6m + m2 = 5

The m term is 6m.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6m + 9 + m2 = 5 + 9

Reorder the terms:
9 + 6m + m2 = 5 + 9

Combine like terms: 5 + 9 = 14
9 + 6m + m2 = 14

Factor a perfect square on the left side:
(m + 3)(m + 3) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(m + 3) equal to 3.741657387 and -3.741657387.

Subproblem 1
m + 3 = 3.741657387

Simplifying
m + 3 = 3.741657387

Reorder the terms:
3 + m = 3.741657387

Solving
3 + m = 3.741657387

Solving for variable 'm'.

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

Add '-3' to each side of the equation.
3 + -3 + m = 3.741657387 + -3

Combine like terms: 3 + -3 = 0
0 + m = 3.741657387 + -3
m = 3.741657387 + -3

Combine like terms: 3.741657387 + -3 = 0.741657387
m = 0.741657387

Simplifying
m = 0.741657387

Subproblem 2
m + 3 = -3.741657387

Simplifying
m + 3 = -3.741657387

Reorder the terms:
3 + m = -3.741657387

Solving
3 + m = -3.741657387

Solving for variable 'm'.

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

Add '-3' to each side of the equation.
3 + -3 + m = -3.741657387 + -3

Combine like terms: 3 + -3 = 0
0 + m = -3.741657387 + -3
m = -3.741657387 + -3

Combine like terms: -3.741657387 + -3 = -6.741657387
m = -6.741657387

Simplifying
m = -6.741657387

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.741657387, -6.741657387}