m^2+8m-5=0

Solution for m^2+8m-5=0 equation:

Simplifying
m2 + 8m + -5 = 0

Reorder the terms:
-5 + 8m + m2 = 0

Solving
-5 + 8m + 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 + 8m + 5 + m2 = 0 + 5

Reorder the terms:
-5 + 5 + 8m + m2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 8m + m2 = 0 + 5
8m + m2 = 0 + 5

Combine like terms: 0 + 5 = 5
8m + m2 = 5

The m term is 8m.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8m + 16 + m2 = 5 + 16

Reorder the terms:
16 + 8m + m2 = 5 + 16

Combine like terms: 5 + 16 = 21
16 + 8m + m2 = 21

Factor a perfect square on the left side:
(m + 4)(m + 4) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(m + 4) equal to 4.582575695 and -4.582575695.

Subproblem 1
m + 4 = 4.582575695

Simplifying
m + 4 = 4.582575695

Reorder the terms:
4 + m = 4.582575695

Solving
4 + m = 4.582575695

Solving for variable 'm'.

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

Add '-4' to each side of the equation.
4 + -4 + m = 4.582575695 + -4

Combine like terms: 4 + -4 = 0
0 + m = 4.582575695 + -4
m = 4.582575695 + -4

Combine like terms: 4.582575695 + -4 = 0.582575695
m = 0.582575695

Simplifying
m = 0.582575695

Subproblem 2
m + 4 = -4.582575695

Simplifying
m + 4 = -4.582575695

Reorder the terms:
4 + m = -4.582575695

Solving
4 + m = -4.582575695

Solving for variable 'm'.

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

Add '-4' to each side of the equation.
4 + -4 + m = -4.582575695 + -4

Combine like terms: 4 + -4 = 0
0 + m = -4.582575695 + -4
m = -4.582575695 + -4

Combine like terms: -4.582575695 + -4 = -8.582575695
m = -8.582575695

Simplifying
m = -8.582575695

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.582575695, -8.582575695}