(r-2)(r+8)=55

Solution for (r-2)(r+8)=55 equation:

Simplifying
(r + -2)(r + 8) = 55

Reorder the terms:
(-2 + r)(r + 8) = 55

Reorder the terms:
(-2 + r)(8 + r) = 55

Multiply (-2 + r) * (8 + r)
(-2(8 + r) + r(8 + r)) = 55
((8 * -2 + r * -2) + r(8 + r)) = 55
((-16 + -2r) + r(8 + r)) = 55
(-16 + -2r + (8 * r + r * r)) = 55
(-16 + -2r + (8r + r2)) = 55

Combine like terms: -2r + 8r = 6r
(-16 + 6r + r2) = 55

Solving
-16 + 6r + r2 = 55

Solving for variable 'r'.

Reorder the terms:
-16 + -55 + 6r + r2 = 55 + -55

Combine like terms: -16 + -55 = -71
-71 + 6r + r2 = 55 + -55

Combine like terms: 55 + -55 = 0
-71 + 6r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '71' to each side of the equation.
-71 + 6r + 71 + r2 = 0 + 71

Reorder the terms:
-71 + 71 + 6r + r2 = 0 + 71

Combine like terms: -71 + 71 = 0
0 + 6r + r2 = 0 + 71
6r + r2 = 0 + 71

Combine like terms: 0 + 71 = 71
6r + r2 = 71

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 = 71 + 9

Reorder the terms:
9 + 6r + r2 = 71 + 9

Combine like terms: 71 + 9 = 80
9 + 6r + r2 = 80

Factor a perfect square on the left side:
(r + 3)(r + 3) = 80

Calculate the square root of the right side: 8.94427191

Break this problem into two subproblems by setting 
(r + 3) equal to 8.94427191 and -8.94427191.

Subproblem 1
r + 3 = 8.94427191

Simplifying
r + 3 = 8.94427191

Reorder the terms:
3 + r = 8.94427191

Solving
3 + r = 8.94427191

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 = 8.94427191 + -3

Combine like terms: 3 + -3 = 0
0 + r = 8.94427191 + -3
r = 8.94427191 + -3

Combine like terms: 8.94427191 + -3 = 5.94427191
r = 5.94427191

Simplifying
r = 5.94427191

Subproblem 2
r + 3 = -8.94427191

Simplifying
r + 3 = -8.94427191

Reorder the terms:
3 + r = -8.94427191

Solving
3 + r = -8.94427191

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 = -8.94427191 + -3

Combine like terms: 3 + -3 = 0
0 + r = -8.94427191 + -3
r = -8.94427191 + -3

Combine like terms: -8.94427191 + -3 = -11.94427191
r = -11.94427191

Simplifying
r = -11.94427191

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {5.94427191, -11.94427191}