m^2+10m+1=0

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

Simplifying
m2 + 10m + 1 = 0

Reorder the terms:
1 + 10m + m2 = 0

Solving
1 + 10m + 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 + 10m + -1 + m2 = 0 + -1

Reorder the terms:
1 + -1 + 10m + m2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 10m + m2 = 0 + -1
10m + m2 = 0 + -1

Combine like terms: 0 + -1 = -1
10m + m2 = -1

The m term is 10m.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10m + 25 + m2 = -1 + 25

Reorder the terms:
25 + 10m + m2 = -1 + 25

Combine like terms: -1 + 25 = 24
25 + 10m + m2 = 24

Factor a perfect square on the left side:
(m + 5)(m + 5) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(m + 5) equal to 4.898979486 and -4.898979486.

Subproblem 1
m + 5 = 4.898979486

Simplifying
m + 5 = 4.898979486

Reorder the terms:
5 + m = 4.898979486

Solving
5 + m = 4.898979486

Solving for variable 'm'.

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

Add '-5' to each side of the equation.
5 + -5 + m = 4.898979486 + -5

Combine like terms: 5 + -5 = 0
0 + m = 4.898979486 + -5
m = 4.898979486 + -5

Combine like terms: 4.898979486 + -5 = -0.101020514
m = -0.101020514

Simplifying
m = -0.101020514

Subproblem 2
m + 5 = -4.898979486

Simplifying
m + 5 = -4.898979486

Reorder the terms:
5 + m = -4.898979486

Solving
5 + m = -4.898979486

Solving for variable 'm'.

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

Add '-5' to each side of the equation.
5 + -5 + m = -4.898979486 + -5

Combine like terms: 5 + -5 = 0
0 + m = -4.898979486 + -5
m = -4.898979486 + -5

Combine like terms: -4.898979486 + -5 = -9.898979486
m = -9.898979486

Simplifying
m = -9.898979486

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.101020514, -9.898979486}