r^2-2r-39=0

Solution for r^2-2r-39=0 equation:

Simplifying
r2 + -2r + -39 = 0

Reorder the terms:
-39 + -2r + r2 = 0

Solving
-39 + -2r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '39' to each side of the equation.
-39 + -2r + 39 + r2 = 0 + 39

Reorder the terms:
-39 + 39 + -2r + r2 = 0 + 39

Combine like terms: -39 + 39 = 0
0 + -2r + r2 = 0 + 39
-2r + r2 = 0 + 39

Combine like terms: 0 + 39 = 39
-2r + r2 = 39

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

Add '1' to each side of the equation.
-2r + 1 + r2 = 39 + 1

Reorder the terms:
1 + -2r + r2 = 39 + 1

Combine like terms: 39 + 1 = 40
1 + -2r + r2 = 40

Factor a perfect square on the left side:
(r + -1)(r + -1) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(r + -1) equal to 6.32455532 and -6.32455532.

Subproblem 1
r + -1 = 6.32455532

Simplifying
r + -1 = 6.32455532

Reorder the terms:
-1 + r = 6.32455532

Solving
-1 + r = 6.32455532

Solving for variable 'r'.

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

Add '1' to each side of the equation.
-1 + 1 + r = 6.32455532 + 1

Combine like terms: -1 + 1 = 0
0 + r = 6.32455532 + 1
r = 6.32455532 + 1

Combine like terms: 6.32455532 + 1 = 7.32455532
r = 7.32455532

Simplifying
r = 7.32455532

Subproblem 2
r + -1 = -6.32455532

Simplifying
r + -1 = -6.32455532

Reorder the terms:
-1 + r = -6.32455532

Solving
-1 + r = -6.32455532

Solving for variable 'r'.

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

Add '1' to each side of the equation.
-1 + 1 + r = -6.32455532 + 1

Combine like terms: -1 + 1 = 0
0 + r = -6.32455532 + 1
r = -6.32455532 + 1

Combine like terms: -6.32455532 + 1 = -5.32455532
r = -5.32455532

Simplifying
r = -5.32455532

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {7.32455532, -5.32455532}