6611.584=2(3.14*r^2)+2*3.14*r*61.2

Solution for 6611.584=2(3.14*r^2)+2*3.14*r*61.2 equation:

Simplifying
6611.584 = 2(3.14r2) + 2 * 3.14r * 61.2

Remove parenthesis around (3.14r2)
6611.584 = 2 * 3.14r2 + 2 * 3.14r * 61.2

Multiply 2 * 3.14
6611.584 = 6.28r2 + 2 * 3.14r * 61.2

Reorder the terms for easier multiplication:
6611.584 = 6.28r2 + 2 * 3.14 * 61.2r

Multiply 2 * 3.14
6611.584 = 6.28r2 + 6.28 * 61.2r

Multiply 6.28 * 61.2
6611.584 = 6.28r2 + 384.336r

Reorder the terms:
6611.584 = 384.336r + 6.28r2

Solving
6611.584 = 384.336r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
6611.584 + -384.336r + -6.28r2 = 384.336r + -384.336r + 6.28r2 + -6.28r2

Combine like terms: 384.336r + -384.336r = 0.000
6611.584 + -384.336r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
6611.584 + -384.336r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
6611.584 + -384.336r + -6.28r2 = 0.00

Begin completing the square.  Divide all terms by
-6.28 the coefficient of the squared term: 

Divide each side by '-6.28'.
-1052.8 + 61.2r + r2 = 0

Move the constant term to the right:

Add '1052.8' to each side of the equation.
-1052.8 + 61.2r + 1052.8 + r2 = 0 + 1052.8

Reorder the terms:
-1052.8 + 1052.8 + 61.2r + r2 = 0 + 1052.8

Combine like terms: -1052.8 + 1052.8 = 0.0
0.0 + 61.2r + r2 = 0 + 1052.8
61.2r + r2 = 0 + 1052.8

Combine like terms: 0 + 1052.8 = 1052.8
61.2r + r2 = 1052.8

The r term is 61.2r.  Take half its coefficient (30.6).
Square it (936.36) and add it to both sides.

Add '936.36' to each side of the equation.
61.2r + 936.36 + r2 = 1052.8 + 936.36

Reorder the terms:
936.36 + 61.2r + r2 = 1052.8 + 936.36

Combine like terms: 1052.8 + 936.36 = 1989.16
936.36 + 61.2r + r2 = 1989.16

Factor a perfect square on the left side:
(r + 30.6)(r + 30.6) = 1989.16

Calculate the square root of the right side: 44.6

Break this problem into two subproblems by setting 
(r + 30.6) equal to 44.6 and -44.6.

Subproblem 1
r + 30.6 = 44.6

Simplifying
r + 30.6 = 44.6

Reorder the terms:
30.6 + r = 44.6

Solving
30.6 + r = 44.6

Solving for variable 'r'.

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

Add '-30.6' to each side of the equation.
30.6 + -30.6 + r = 44.6 + -30.6

Combine like terms: 30.6 + -30.6 = 0.0
0.0 + r = 44.6 + -30.6
r = 44.6 + -30.6

Combine like terms: 44.6 + -30.6 = 14
r = 14

Simplifying
r = 14

Subproblem 2
r + 30.6 = -44.6

Simplifying
r + 30.6 = -44.6

Reorder the terms:
30.6 + r = -44.6

Solving
30.6 + r = -44.6

Solving for variable 'r'.

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

Add '-30.6' to each side of the equation.
30.6 + -30.6 + r = -44.6 + -30.6

Combine like terms: 30.6 + -30.6 = 0.0
0.0 + r = -44.6 + -30.6
r = -44.6 + -30.6

Combine like terms: -44.6 + -30.6 = -75.2
r = -75.2

Simplifying
r = -75.2

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {14, -75.2}