r^2-6r-4=0

Solution for r^2-6r-4=0 equation:

Simplifying
r2 + -6r + -4 = 0

Reorder the terms:
-4 + -6r + r2 = 0

Solving
-4 + -6r + 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 + -6r + 4 + r2 = 0 + 4

Reorder the terms:
-4 + 4 + -6r + r2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -6r + r2 = 0 + 4
-6r + r2 = 0 + 4

Combine like terms: 0 + 4 = 4
-6r + r2 = 4

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

Add '9' to each side of the equation.
-6r + 9 + r2 = 4 + 9

Reorder the terms:
9 + -6r + r2 = 4 + 9

Combine like terms: 4 + 9 = 13
9 + -6r + r2 = 13

Factor a perfect square on the left side:
(r + -3)(r + -3) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(r + -3) equal to 3.605551275 and -3.605551275.

Subproblem 1
r + -3 = 3.605551275

Simplifying
r + -3 = 3.605551275

Reorder the terms:
-3 + r = 3.605551275

Solving
-3 + r = 3.605551275

Solving for variable 'r'.

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

Add '3' to each side of the equation.
-3 + 3 + r = 3.605551275 + 3

Combine like terms: -3 + 3 = 0
0 + r = 3.605551275 + 3
r = 3.605551275 + 3

Combine like terms: 3.605551275 + 3 = 6.605551275
r = 6.605551275

Simplifying
r = 6.605551275

Subproblem 2
r + -3 = -3.605551275

Simplifying
r + -3 = -3.605551275

Reorder the terms:
-3 + r = -3.605551275

Solving
-3 + r = -3.605551275

Solving for variable 'r'.

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

Add '3' to each side of the equation.
-3 + 3 + r = -3.605551275 + 3

Combine like terms: -3 + 3 = 0
0 + r = -3.605551275 + 3
r = -3.605551275 + 3

Combine like terms: -3.605551275 + 3 = -0.605551275
r = -0.605551275

Simplifying
r = -0.605551275

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {6.605551275, -0.605551275}