52611.328=6.28r^2+1514.736r

Solution for 52611.328=6.28r^2+1514.736r equation:

Simplifying
52611.328 = 6.28r2 + 1514.736r

Reorder the terms:
52611.328 = 1514.736r + 6.28r2

Solving
52611.328 = 1514.736r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
52611.328 + -1514.736r + -6.28r2 = 1514.736r + -1514.736r + 6.28r2 + -6.28r2

Combine like terms: 1514.736r + -1514.736r = 0.000
52611.328 + -1514.736r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
52611.328 + -1514.736r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
52611.328 + -1514.736r + -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'.
-8377.6 + 241.2r + r2 = 0

Move the constant term to the right:

Add '8377.6' to each side of the equation.
-8377.6 + 241.2r + 8377.6 + r2 = 0 + 8377.6

Reorder the terms:
-8377.6 + 8377.6 + 241.2r + r2 = 0 + 8377.6

Combine like terms: -8377.6 + 8377.6 = 0.0
0.0 + 241.2r + r2 = 0 + 8377.6
241.2r + r2 = 0 + 8377.6

Combine like terms: 0 + 8377.6 = 8377.6
241.2r + r2 = 8377.6

The r term is 241.2r.  Take half its coefficient (120.6).
Square it (14544.36) and add it to both sides.

Add '14544.36' to each side of the equation.
241.2r + 14544.36 + r2 = 8377.6 + 14544.36

Reorder the terms:
14544.36 + 241.2r + r2 = 8377.6 + 14544.36

Combine like terms: 8377.6 + 14544.36 = 22921.96
14544.36 + 241.2r + r2 = 22921.96

Factor a perfect square on the left side:
(r + 120.6)(r + 120.6) = 22921.96

Calculate the square root of the right side: 151.4

Break this problem into two subproblems by setting 
(r + 120.6) equal to 151.4 and -151.4.

Subproblem 1
r + 120.6 = 151.4

Simplifying
r + 120.6 = 151.4

Reorder the terms:
120.6 + r = 151.4

Solving
120.6 + r = 151.4

Solving for variable 'r'.

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

Add '-120.6' to each side of the equation.
120.6 + -120.6 + r = 151.4 + -120.6

Combine like terms: 120.6 + -120.6 = 0.0
0.0 + r = 151.4 + -120.6
r = 151.4 + -120.6

Combine like terms: 151.4 + -120.6 = 30.8
r = 30.8

Simplifying
r = 30.8

Subproblem 2
r + 120.6 = -151.4

Simplifying
r + 120.6 = -151.4

Reorder the terms:
120.6 + r = -151.4

Solving
120.6 + r = -151.4

Solving for variable 'r'.

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

Add '-120.6' to each side of the equation.
120.6 + -120.6 + r = -151.4 + -120.6

Combine like terms: 120.6 + -120.6 = 0.0
0.0 + r = -151.4 + -120.6
r = -151.4 + -120.6

Combine like terms: -151.4 + -120.6 = -272
r = -272

Simplifying
r = -272

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {30.8, -272}