m^2+8m-59=0

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Solution for m^2+8m-59=0 equation: 


Simplifying
m2 + 8m + -59 = 0

Reorder the terms:
-59 + 8m + m2 = 0

Solving
-59 + 8m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '59' to each side of the equation.
-59 + 8m + 59 + m2 = 0 + 59

Reorder the terms:
-59 + 59 + 8m + m2 = 0 + 59

Combine like terms: -59 + 59 = 0
0 + 8m + m2 = 0 + 59
8m + m2 = 0 + 59

Combine like terms: 0 + 59 = 59
8m + m2 = 59

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 = 59 + 16

Reorder the terms:
16 + 8m + m2 = 59 + 16

Combine like terms: 59 + 16 = 75
16 + 8m + m2 = 75

Factor a perfect square on the left side:
(m + 4)(m + 4) = 75

Calculate the square root of the right side: 8.660254038

Break this problem into two subproblems by setting 
(m + 4) equal to 8.660254038 and -8.660254038.


Subproblem 1
m + 4 = 8.660254038

Simplifying
m + 4 = 8.660254038

Reorder the terms:
4 + m = 8.660254038

Solving
4 + m = 8.660254038

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 = 8.660254038 + -4

Combine like terms: 4 + -4 = 0
0 + m = 8.660254038 + -4
m = 8.660254038 + -4

Combine like terms: 8.660254038 + -4 = 4.660254038
m = 4.660254038

Simplifying
m = 4.660254038


Subproblem 2
m + 4 = -8.660254038

Simplifying
m + 4 = -8.660254038

Reorder the terms:
4 + m = -8.660254038

Solving
4 + m = -8.660254038

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 = -8.660254038 + -4

Combine like terms: 4 + -4 = 0
0 + m = -8.660254038 + -4
m = -8.660254038 + -4

Combine like terms: -8.660254038 + -4 = -12.660254038
m = -12.660254038

Simplifying
m = -12.660254038


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {4.660254038, -12.660254038}

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