(4m^2)+10m+1=0

Solution for (4m^2)+10m+1=0 equation:

Simplifying
(4m2) + 10m + 1 = 0

Reorder the terms:
1 + 10m + (4m2) = 0

Solving
1 + 10m + (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 + 2.5m + m2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + 2.5m + -0.25 + m2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + 2.5m + m2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + 2.5m + m2 = 0 + -0.25
2.5m + m2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
2.5m + m2 = -0.25

The m term is 2.5m.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5m + 1.5625 + m2 = -0.25 + 1.5625

Reorder the terms:
1.5625 + 2.5m + m2 = -0.25 + 1.5625

Combine like terms: -0.25 + 1.5625 = 1.3125
1.5625 + 2.5m + m2 = 1.3125

Factor a perfect square on the left side:
((m) + 1.25)((m) + 1.25) = 1.3125

Calculate the square root of the right side: 1.145643924

Break this problem into two subproblems by setting 
((m) + 1.25) equal to 1.145643924 and -1.145643924.

Subproblem 1
(m) + 1.25 = 1.145643924

Simplifying
(m) + 1.25 = 1.145643924
m + 1.25 = 1.145643924

Reorder the terms:
1.25 + m = 1.145643924

Solving
1.25 + m = 1.145643924

Solving for variable 'm'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + m = 1.145643924 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + m = 1.145643924 + -1.25
m = 1.145643924 + -1.25

Combine like terms: 1.145643924 + -1.25 = -0.104356076
m = -0.104356076

Simplifying
m = -0.104356076

Subproblem 2
(m) + 1.25 = -1.145643924

Simplifying
(m) + 1.25 = -1.145643924
m + 1.25 = -1.145643924

Reorder the terms:
1.25 + m = -1.145643924

Solving
1.25 + m = -1.145643924

Solving for variable 'm'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + m = -1.145643924 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + m = -1.145643924 + -1.25
m = -1.145643924 + -1.25

Combine like terms: -1.145643924 + -1.25 = -2.395643924
m = -2.395643924

Simplifying
m = -2.395643924

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.104356076, -2.395643924}