m^2+4m+1=0

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

Simplifying
m2 + 4m + 1 = 0

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

Solving
1 + 4m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 4m + -1 + m2 = 0 + -1

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

Combine like terms: 1 + -1 = 0
0 + 4m + m2 = 0 + -1
4m + m2 = 0 + -1

Combine like terms: 0 + -1 = -1
4m + m2 = -1

The m term is 4m.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4m + 4 + m2 = -1 + 4

Reorder the terms:
4 + 4m + m2 = -1 + 4

Combine like terms: -1 + 4 = 3
4 + 4m + m2 = 3

Factor a perfect square on the left side:
(m + 2)(m + 2) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(m + 2) equal to 1.732050808 and -1.732050808.

Subproblem 1
m + 2 = 1.732050808

Simplifying
m + 2 = 1.732050808

Reorder the terms:
2 + m = 1.732050808

Solving
2 + m = 1.732050808

Solving for variable 'm'.

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

Add '-2' to each side of the equation.
2 + -2 + m = 1.732050808 + -2

Combine like terms: 2 + -2 = 0
0 + m = 1.732050808 + -2
m = 1.732050808 + -2

Combine like terms: 1.732050808 + -2 = -0.267949192
m = -0.267949192

Simplifying
m = -0.267949192

Subproblem 2
m + 2 = -1.732050808

Simplifying
m + 2 = -1.732050808

Reorder the terms:
2 + m = -1.732050808

Solving
2 + m = -1.732050808

Solving for variable 'm'.

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

Add '-2' to each side of the equation.
2 + -2 + m = -1.732050808 + -2

Combine like terms: 2 + -2 = 0
0 + m = -1.732050808 + -2
m = -1.732050808 + -2

Combine like terms: -1.732050808 + -2 = -3.732050808
m = -3.732050808

Simplifying
m = -3.732050808

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.267949192, -3.732050808}