m^2-2m-34=0

Solution for m^2-2m-34=0 equation:

Simplifying
m2 + -2m + -34 = 0

Reorder the terms:
-34 + -2m + m2 = 0

Solving
-34 + -2m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '34' to each side of the equation.
-34 + -2m + 34 + m2 = 0 + 34

Reorder the terms:
-34 + 34 + -2m + m2 = 0 + 34

Combine like terms: -34 + 34 = 0
0 + -2m + m2 = 0 + 34
-2m + m2 = 0 + 34

Combine like terms: 0 + 34 = 34
-2m + m2 = 34

The m term is -2m.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2m + 1 + m2 = 34 + 1

Reorder the terms:
1 + -2m + m2 = 34 + 1

Combine like terms: 34 + 1 = 35
1 + -2m + m2 = 35

Factor a perfect square on the left side:
(m + -1)(m + -1) = 35

Calculate the square root of the right side: 5.916079783

Break this problem into two subproblems by setting 
(m + -1) equal to 5.916079783 and -5.916079783.

Subproblem 1
m + -1 = 5.916079783

Simplifying
m + -1 = 5.916079783

Reorder the terms:
-1 + m = 5.916079783

Solving
-1 + m = 5.916079783

Solving for variable 'm'.

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

Add '1' to each side of the equation.
-1 + 1 + m = 5.916079783 + 1

Combine like terms: -1 + 1 = 0
0 + m = 5.916079783 + 1
m = 5.916079783 + 1

Combine like terms: 5.916079783 + 1 = 6.916079783
m = 6.916079783

Simplifying
m = 6.916079783

Subproblem 2
m + -1 = -5.916079783

Simplifying
m + -1 = -5.916079783

Reorder the terms:
-1 + m = -5.916079783

Solving
-1 + m = -5.916079783

Solving for variable 'm'.

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

Add '1' to each side of the equation.
-1 + 1 + m = -5.916079783 + 1

Combine like terms: -1 + 1 = 0
0 + m = -5.916079783 + 1
m = -5.916079783 + 1

Combine like terms: -5.916079783 + 1 = -4.916079783
m = -4.916079783

Simplifying
m = -4.916079783

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {6.916079783, -4.916079783}