m^2-6m-26=0

Solution for m^2-6m-26=0 equation:

Simplifying
m2 + -6m + -26 = 0

Reorder the terms:
-26 + -6m + m2 = 0

Solving
-26 + -6m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + -6m + 26 + m2 = 0 + 26

Reorder the terms:
-26 + 26 + -6m + m2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + -6m + m2 = 0 + 26
-6m + m2 = 0 + 26

Combine like terms: 0 + 26 = 26
-6m + m2 = 26

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 = 26 + 9

Reorder the terms:
9 + -6m + m2 = 26 + 9

Combine like terms: 26 + 9 = 35
9 + -6m + m2 = 35

Factor a perfect square on the left side:
(m + -3)(m + -3) = 35

Calculate the square root of the right side: 5.916079783

Break this problem into two subproblems by setting 
(m + -3) equal to 5.916079783 and -5.916079783.

Subproblem 1
m + -3 = 5.916079783

Simplifying
m + -3 = 5.916079783

Reorder the terms:
-3 + m = 5.916079783

Solving
-3 + m = 5.916079783

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 = 5.916079783 + 3

Combine like terms: -3 + 3 = 0
0 + m = 5.916079783 + 3
m = 5.916079783 + 3

Combine like terms: 5.916079783 + 3 = 8.916079783
m = 8.916079783

Simplifying
m = 8.916079783

Subproblem 2
m + -3 = -5.916079783

Simplifying
m + -3 = -5.916079783

Reorder the terms:
-3 + m = -5.916079783

Solving
-3 + m = -5.916079783

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 = -5.916079783 + 3

Combine like terms: -3 + 3 = 0
0 + m = -5.916079783 + 3
m = -5.916079783 + 3

Combine like terms: -5.916079783 + 3 = -2.916079783
m = -2.916079783

Simplifying
m = -2.916079783

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {8.916079783, -2.916079783}