r^2-2r-4=0

Solution for r^2-2r-4=0 equation:

Simplifying
r2 + -2r + -4 = 0

Reorder the terms:
-4 + -2r + r2 = 0

Solving
-4 + -2r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -2r + 4 + r2 = 0 + 4

Reorder the terms:
-4 + 4 + -2r + r2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -2r + r2 = 0 + 4
-2r + r2 = 0 + 4

Combine like terms: 0 + 4 = 4
-2r + r2 = 4

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 = 4 + 1

Reorder the terms:
1 + -2r + r2 = 4 + 1

Combine like terms: 4 + 1 = 5
1 + -2r + r2 = 5

Factor a perfect square on the left side:
(r + -1)(r + -1) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(r + -1) equal to 2.236067978 and -2.236067978.

Subproblem 1
r + -1 = 2.236067978

Simplifying
r + -1 = 2.236067978

Reorder the terms:
-1 + r = 2.236067978

Solving
-1 + r = 2.236067978

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 = 2.236067978 + 1

Combine like terms: -1 + 1 = 0
0 + r = 2.236067978 + 1
r = 2.236067978 + 1

Combine like terms: 2.236067978 + 1 = 3.236067978
r = 3.236067978

Simplifying
r = 3.236067978

Subproblem 2
r + -1 = -2.236067978

Simplifying
r + -1 = -2.236067978

Reorder the terms:
-1 + r = -2.236067978

Solving
-1 + r = -2.236067978

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 = -2.236067978 + 1

Combine like terms: -1 + 1 = 0
0 + r = -2.236067978 + 1
r = -2.236067978 + 1

Combine like terms: -2.236067978 + 1 = -1.236067978
r = -1.236067978

Simplifying
r = -1.236067978

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {3.236067978, -1.236067978}