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 = 9.898979486
m = 9.898979486

Simplifying
m = 9.898979486

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 = 0.101020514
m = 0.101020514

Simplifying
m = 0.101020514

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