m^2+8m+3=0

Solution for m^2+8m+3=0 equation:

Simplifying
m2 + 8m + 3 = 0

Reorder the terms:
3 + 8m + m2 = 0

Solving
3 + 8m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 8m + -3 + m2 = 0 + -3

Reorder the terms:
3 + -3 + 8m + m2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 8m + m2 = 0 + -3
8m + m2 = 0 + -3

Combine like terms: 0 + -3 = -3
8m + m2 = -3

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 = -3 + 16

Reorder the terms:
16 + 8m + m2 = -3 + 16

Combine like terms: -3 + 16 = 13
16 + 8m + m2 = 13

Factor a perfect square on the left side:
(m + 4)(m + 4) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(m + 4) equal to 3.605551275 and -3.605551275.

Subproblem 1
m + 4 = 3.605551275

Simplifying
m + 4 = 3.605551275

Reorder the terms:
4 + m = 3.605551275

Solving
4 + m = 3.605551275

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 = 3.605551275 + -4

Combine like terms: 4 + -4 = 0
0 + m = 3.605551275 + -4
m = 3.605551275 + -4

Combine like terms: 3.605551275 + -4 = -0.394448725
m = -0.394448725

Simplifying
m = -0.394448725

Subproblem 2
m + 4 = -3.605551275

Simplifying
m + 4 = -3.605551275

Reorder the terms:
4 + m = -3.605551275

Solving
4 + m = -3.605551275

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 = -3.605551275 + -4

Combine like terms: 4 + -4 = 0
0 + m = -3.605551275 + -4
m = -3.605551275 + -4

Combine like terms: -3.605551275 + -4 = -7.605551275
m = -7.605551275

Simplifying
m = -7.605551275

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.394448725, -7.605551275}