4m^2+8m+1=0

Solution for 4m^2+8m+1=0 equation:

Simplifying
4m2 + 8m + 1 = 0

Reorder the terms:
1 + 8m + 4m2 = 0

Solving
1 + 8m + 4m2 = 0

Solving for variable 'm'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
0.25 + 2m + m2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + 2m + -0.25 + m2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + 2m + m2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + 2m + m2 = 0 + -0.25
2m + m2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
2m + m2 = -0.25

The m term is 2m.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2m + 1 + m2 = -0.25 + 1

Reorder the terms:
1 + 2m + m2 = -0.25 + 1

Combine like terms: -0.25 + 1 = 0.75
1 + 2m + m2 = 0.75

Factor a perfect square on the left side:
(m + 1)(m + 1) = 0.75

Calculate the square root of the right side: 0.866025404

Break this problem into two subproblems by setting 
(m + 1) equal to 0.866025404 and -0.866025404.

Subproblem 1
m + 1 = 0.866025404

Simplifying
m + 1 = 0.866025404

Reorder the terms:
1 + m = 0.866025404

Solving
1 + m = 0.866025404

Solving for variable 'm'.

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

Add '-1' to each side of the equation.
1 + -1 + m = 0.866025404 + -1

Combine like terms: 1 + -1 = 0
0 + m = 0.866025404 + -1
m = 0.866025404 + -1

Combine like terms: 0.866025404 + -1 = -0.133974596
m = -0.133974596

Simplifying
m = -0.133974596

Subproblem 2
m + 1 = -0.866025404

Simplifying
m + 1 = -0.866025404

Reorder the terms:
1 + m = -0.866025404

Solving
1 + m = -0.866025404

Solving for variable 'm'.

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

Add '-1' to each side of the equation.
1 + -1 + m = -0.866025404 + -1

Combine like terms: 1 + -1 = 0
0 + m = -0.866025404 + -1
m = -0.866025404 + -1

Combine like terms: -0.866025404 + -1 = -1.866025404
m = -1.866025404

Simplifying
m = -1.866025404

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.133974596, -1.866025404}