8.8152=2*3.14r^2+2*3.14r*38.3

Solution for 8.8152=2*3.14r^2+2*3.14r*38.3 equation:

Simplifying
8.8152 = 2 * 3.14r2 + 2 * 3.14r * 38.3

Multiply 2 * 3.14
8.8152 = 6.28r2 + 2 * 3.14r * 38.3

Reorder the terms for easier multiplication:
8.8152 = 6.28r2 + 2 * 3.14 * 38.3r

Multiply 2 * 3.14
8.8152 = 6.28r2 + 6.28 * 38.3r

Multiply 6.28 * 38.3
8.8152 = 6.28r2 + 240.524r

Reorder the terms:
8.8152 = 240.524r + 6.28r2

Solving
8.8152 = 240.524r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
8.8152 + -240.524r + -6.28r2 = 240.524r + -240.524r + 6.28r2 + -6.28r2

Combine like terms: 240.524r + -240.524r = 0.000
8.8152 + -240.524r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
8.8152 + -240.524r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
8.8152 + -240.524r + -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'.
-1.403694268 + 38.3r + r2 = 0

Move the constant term to the right:

Add '1.403694268' to each side of the equation.
-1.403694268 + 38.3r + 1.403694268 + r2 = 0 + 1.403694268

Reorder the terms:
-1.403694268 + 1.403694268 + 38.3r + r2 = 0 + 1.403694268

Combine like terms: -1.403694268 + 1.403694268 = 0.000000000
0.000000000 + 38.3r + r2 = 0 + 1.403694268
38.3r + r2 = 0 + 1.403694268

Combine like terms: 0 + 1.403694268 = 1.403694268
38.3r + r2 = 1.403694268

The r term is 38.3r.  Take half its coefficient (19.15).
Square it (366.7225) and add it to both sides.

Add '366.7225' to each side of the equation.
38.3r + 366.7225 + r2 = 1.403694268 + 366.7225

Reorder the terms:
366.7225 + 38.3r + r2 = 1.403694268 + 366.7225

Combine like terms: 1.403694268 + 366.7225 = 368.126194268
366.7225 + 38.3r + r2 = 368.126194268

Factor a perfect square on the left side:
(r + 19.15)(r + 19.15) = 368.126194268

Calculate the square root of the right side: 19.186614977

Break this problem into two subproblems by setting 
(r + 19.15) equal to 19.186614977 and -19.186614977.

Subproblem 1
r + 19.15 = 19.186614977

Simplifying
r + 19.15 = 19.186614977

Reorder the terms:
19.15 + r = 19.186614977

Solving
19.15 + r = 19.186614977

Solving for variable 'r'.

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

Add '-19.15' to each side of the equation.
19.15 + -19.15 + r = 19.186614977 + -19.15

Combine like terms: 19.15 + -19.15 = 0.00
0.00 + r = 19.186614977 + -19.15
r = 19.186614977 + -19.15

Combine like terms: 19.186614977 + -19.15 = 0.036614977
r = 0.036614977

Simplifying
r = 0.036614977

Subproblem 2
r + 19.15 = -19.186614977

Simplifying
r + 19.15 = -19.186614977

Reorder the terms:
19.15 + r = -19.186614977

Solving
19.15 + r = -19.186614977

Solving for variable 'r'.

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

Add '-19.15' to each side of the equation.
19.15 + -19.15 + r = -19.186614977 + -19.15

Combine like terms: 19.15 + -19.15 = 0.00
0.00 + r = -19.186614977 + -19.15
r = -19.186614977 + -19.15

Combine like terms: -19.186614977 + -19.15 = -38.336614977
r = -38.336614977

Simplifying
r = -38.336614977

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.036614977, -38.336614977}