2708.8152=6.28*r^2+6.28*r*38.3

Solution for 2708.8152=6.28*r^2+6.28*r*38.3 equation:

Simplifying
2708.8152 = 6.28r2 + 6.28r * 38.3

Reorder the terms for easier multiplication:
2708.8152 = 6.28r2 + 6.28 * 38.3r

Multiply 6.28 * 38.3
2708.8152 = 6.28r2 + 240.524r

Reorder the terms:
2708.8152 = 240.524r + 6.28r2

Solving
2708.8152 = 240.524r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
2708.8152 + -240.524r + -6.28r2 = 240.524r + -240.524r + 6.28r2 + -6.28r2

Combine like terms: 240.524r + -240.524r = 0.000
2708.8152 + -240.524r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
2708.8152 + -240.524r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
2708.8152 + -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'.
-431.34 + 38.3r + r2 = 0

Move the constant term to the right:

Add '431.34' to each side of the equation.
-431.34 + 38.3r + 431.34 + r2 = 0 + 431.34

Reorder the terms:
-431.34 + 431.34 + 38.3r + r2 = 0 + 431.34

Combine like terms: -431.34 + 431.34 = 0.00
0.00 + 38.3r + r2 = 0 + 431.34
38.3r + r2 = 0 + 431.34

Combine like terms: 0 + 431.34 = 431.34
38.3r + r2 = 431.34

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 = 431.34 + 366.7225

Reorder the terms:
366.7225 + 38.3r + r2 = 431.34 + 366.7225

Combine like terms: 431.34 + 366.7225 = 798.0625
366.7225 + 38.3r + r2 = 798.0625

Factor a perfect square on the left side:
(r + 19.15)(r + 19.15) = 798.0625

Calculate the square root of the right side: 28.25

Break this problem into two subproblems by setting 
(r + 19.15) equal to 28.25 and -28.25.

Subproblem 1
r + 19.15 = 28.25

Simplifying
r + 19.15 = 28.25

Reorder the terms:
19.15 + r = 28.25

Solving
19.15 + r = 28.25

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 = 28.25 + -19.15

Combine like terms: 19.15 + -19.15 = 0.00
0.00 + r = 28.25 + -19.15
r = 28.25 + -19.15

Combine like terms: 28.25 + -19.15 = 9.1
r = 9.1

Simplifying
r = 9.1

Subproblem 2
r + 19.15 = -28.25

Simplifying
r + 19.15 = -28.25

Reorder the terms:
19.15 + r = -28.25

Solving
19.15 + r = -28.25

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 = -28.25 + -19.15

Combine like terms: 19.15 + -19.15 = 0.00
0.00 + r = -28.25 + -19.15
r = -28.25 + -19.15

Combine like terms: -28.25 + -19.15 = -47.4
r = -47.4

Simplifying
r = -47.4

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {9.1, -47.4}