200(1+2r+r^2)+225+225r=485

Solution for 200(1+2r+r^2)+225+225r=485 equation:

Simplifying
200(1 + 2r + r2) + 225 + 225r = 485
(1 * 200 + 2r * 200 + r2 * 200) + 225 + 225r = 485
(200 + 400r + 200r2) + 225 + 225r = 485

Reorder the terms:
200 + 225 + 400r + 225r + 200r2 = 485

Combine like terms: 200 + 225 = 425
425 + 400r + 225r + 200r2 = 485

Combine like terms: 400r + 225r = 625r
425 + 625r + 200r2 = 485

Solving
425 + 625r + 200r2 = 485

Solving for variable 'r'.

Reorder the terms:
425 + -485 + 625r + 200r2 = 485 + -485

Combine like terms: 425 + -485 = -60
-60 + 625r + 200r2 = 485 + -485

Combine like terms: 485 + -485 = 0
-60 + 625r + 200r2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-12 + 125r + 40r2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-12 + 125r + 40r2)' equal to zero and attempt to solve:

Simplifying
-12 + 125r + 40r2 = 0

Solving
-12 + 125r + 40r2 = 0

Begin completing the square.  Divide all terms by
40 the coefficient of the squared term: 

Divide each side by '40'.
-0.3 + 3.125r + r2 = 0.0

Move the constant term to the right:

Add '0.3' to each side of the equation.
-0.3 + 3.125r + 0.3 + r2 = 0.0 + 0.3

Reorder the terms:
-0.3 + 0.3 + 3.125r + r2 = 0.0 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + 3.125r + r2 = 0.0 + 0.3
3.125r + r2 = 0.0 + 0.3

Combine like terms: 0.0 + 0.3 = 0.3
3.125r + r2 = 0.3

The r term is 3.125r.  Take half its coefficient (1.5625).
Square it (2.44140625) and add it to both sides.

Add '2.44140625' to each side of the equation.
3.125r + 2.44140625 + r2 = 0.3 + 2.44140625

Reorder the terms:
2.44140625 + 3.125r + r2 = 0.3 + 2.44140625

Combine like terms: 0.3 + 2.44140625 = 2.74140625
2.44140625 + 3.125r + r2 = 2.74140625

Factor a perfect square on the left side:
(r + 1.5625)(r + 1.5625) = 2.74140625

Calculate the square root of the right side: 1.655719255

Break this problem into two subproblems by setting 
(r + 1.5625) equal to 1.655719255 and -1.655719255.

Subproblem 1
r + 1.5625 = 1.655719255

Simplifying
r + 1.5625 = 1.655719255

Reorder the terms:
1.5625 + r = 1.655719255

Solving
1.5625 + r = 1.655719255

Solving for variable 'r'.

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

Add '-1.5625' to each side of the equation.
1.5625 + -1.5625 + r = 1.655719255 + -1.5625

Combine like terms: 1.5625 + -1.5625 = 0.0000
0.0000 + r = 1.655719255 + -1.5625
r = 1.655719255 + -1.5625

Combine like terms: 1.655719255 + -1.5625 = 0.093219255
r = 0.093219255

Simplifying
r = 0.093219255

Subproblem 2
r + 1.5625 = -1.655719255

Simplifying
r + 1.5625 = -1.655719255

Reorder the terms:
1.5625 + r = -1.655719255

Solving
1.5625 + r = -1.655719255

Solving for variable 'r'.

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

Add '-1.5625' to each side of the equation.
1.5625 + -1.5625 + r = -1.655719255 + -1.5625

Combine like terms: 1.5625 + -1.5625 = 0.0000
0.0000 + r = -1.655719255 + -1.5625
r = -1.655719255 + -1.5625

Combine like terms: -1.655719255 + -1.5625 = -3.218219255
r = -3.218219255

Simplifying
r = -3.218219255

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.093219255, -3.218219255}
Solution
r = {0.093219255, -3.218219255}