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

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

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

Reorder the terms:
6611.584 = 61.2 + 6.28r + 6.28r2

Solving
6611.584 = 61.2 + 6.28r + 6.28r2

Solving for variable 'r'.

Combine like terms: 6611.584 + -61.2 = 6550.384
6550.384 + -6.28r + -6.28r2 = 61.2 + 6.28r + 6.28r2 + -61.2 + -6.28r + -6.28r2

Reorder the terms:
6550.384 + -6.28r + -6.28r2 = 61.2 + -61.2 + 6.28r + -6.28r + 6.28r2 + -6.28r2

Combine like terms: 61.2 + -61.2 = 0.0
6550.384 + -6.28r + -6.28r2 = 0.0 + 6.28r + -6.28r + 6.28r2 + -6.28r2
6550.384 + -6.28r + -6.28r2 = 6.28r + -6.28r + 6.28r2 + -6.28r2

Combine like terms: 6.28r + -6.28r = 0.00
6550.384 + -6.28r + -6.28r2 = 0.00 + 6.28r2 + -6.28r2
6550.384 + -6.28r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
6550.384 + -6.28r + -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'.
-1043.054777 + r + r2 = 0

Move the constant term to the right:

Add '1043.054777' to each side of the equation.
-1043.054777 + r + 1043.054777 + r2 = 0 + 1043.054777

Reorder the terms:
-1043.054777 + 1043.054777 + r + r2 = 0 + 1043.054777

Combine like terms: -1043.054777 + 1043.054777 = 0.000000
0.000000 + r + r2 = 0 + 1043.054777
r + r2 = 0 + 1043.054777

Combine like terms: 0 + 1043.054777 = 1043.054777
r + r2 = 1043.054777

The r term is r.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + r2 = 1043.054777 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + r2 = 1043.054777 + 0.25

Combine like terms: 1043.054777 + 0.25 = 1043.304777
1.25 + r2 = 1043.304777

Factor a perfect square on the left side:
(r + 0.5)(r + 0.5) = 1043.304777

Calculate the square root of the right side: 32.300228745

Break this problem into two subproblems by setting 
(r + 0.5) equal to 32.300228745 and -32.300228745.

Subproblem 1
r + 0.5 = 32.300228745

Simplifying
r + 0.5 = 32.300228745

Reorder the terms:
0.5 + r = 32.300228745

Solving
0.5 + r = 32.300228745

Solving for variable 'r'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + r = 32.300228745 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = 32.300228745 + -0.5
r = 32.300228745 + -0.5

Combine like terms: 32.300228745 + -0.5 = 31.800228745
r = 31.800228745

Simplifying
r = 31.800228745

Subproblem 2
r + 0.5 = -32.300228745

Simplifying
r + 0.5 = -32.300228745

Reorder the terms:
0.5 + r = -32.300228745

Solving
0.5 + r = -32.300228745

Solving for variable 'r'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + r = -32.300228745 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = -32.300228745 + -0.5
r = -32.300228745 + -0.5

Combine like terms: -32.300228745 + -0.5 = -32.800228745
r = -32.800228745

Simplifying
r = -32.800228745

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {31.800228745, -32.800228745}