m^2-6m-1=0

Solution for m^2-6m-1=0 equation:

Simplifying
m2 + -6m + -1 = 0

Reorder the terms:
-1 + -6m + m2 = 0

Solving
-1 + -6m + 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 + -6m + 1 + m2 = 0 + 1

Reorder the terms:
-1 + 1 + -6m + m2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -6m + m2 = 0 + 1
-6m + m2 = 0 + 1

Combine like terms: 0 + 1 = 1
-6m + m2 = 1

The m term is -6m.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6m + 9 + m2 = 1 + 9

Reorder the terms:
9 + -6m + m2 = 1 + 9

Combine like terms: 1 + 9 = 10
9 + -6m + m2 = 10

Factor a perfect square on the left side:
(m + -3)(m + -3) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(m + -3) equal to 3.16227766 and -3.16227766.

Subproblem 1
m + -3 = 3.16227766

Simplifying
m + -3 = 3.16227766

Reorder the terms:
-3 + m = 3.16227766

Solving
-3 + m = 3.16227766

Solving for variable 'm'.

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

Add '3' to each side of the equation.
-3 + 3 + m = 3.16227766 + 3

Combine like terms: -3 + 3 = 0
0 + m = 3.16227766 + 3
m = 3.16227766 + 3

Combine like terms: 3.16227766 + 3 = 6.16227766
m = 6.16227766

Simplifying
m = 6.16227766

Subproblem 2
m + -3 = -3.16227766

Simplifying
m + -3 = -3.16227766

Reorder the terms:
-3 + m = -3.16227766

Solving
-3 + m = -3.16227766

Solving for variable 'm'.

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

Add '3' to each side of the equation.
-3 + 3 + m = -3.16227766 + 3

Combine like terms: -3 + 3 = 0
0 + m = -3.16227766 + 3
m = -3.16227766 + 3

Combine like terms: -3.16227766 + 3 = -0.16227766
m = -0.16227766

Simplifying
m = -0.16227766

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {6.16227766, -0.16227766}