0=6.28r^2+401.1922r-8038.4

Solution for 0=6.28r^2+401.1922r-8038.4 equation:

Simplifying
0 = 6.28r2 + 401.1922r + -8038.4

Reorder the terms:
0 = -8038.4 + 401.1922r + 6.28r2

Solving
0 = -8038.4 + 401.1922r + 6.28r2

Solving for variable 'r'.

Combine like terms: 0 + 8038.4 = 8038.4
8038.4 + -401.1922r + -6.28r2 = -8038.4 + 401.1922r + 6.28r2 + 8038.4 + -401.1922r + -6.28r2

Reorder the terms:
8038.4 + -401.1922r + -6.28r2 = -8038.4 + 8038.4 + 401.1922r + -401.1922r + 6.28r2 + -6.28r2

Combine like terms: -8038.4 + 8038.4 = 0.0
8038.4 + -401.1922r + -6.28r2 = 0.0 + 401.1922r + -401.1922r + 6.28r2 + -6.28r2
8038.4 + -401.1922r + -6.28r2 = 401.1922r + -401.1922r + 6.28r2 + -6.28r2

Combine like terms: 401.1922r + -401.1922r = 0.0000
8038.4 + -401.1922r + -6.28r2 = 0.0000 + 6.28r2 + -6.28r2
8038.4 + -401.1922r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
8038.4 + -401.1922r + -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'.
-1280 + 63.88410828r + r2 = 0

Move the constant term to the right:

Add '1280' to each side of the equation.
-1280 + 63.88410828r + 1280 + r2 = 0 + 1280

Reorder the terms:
-1280 + 1280 + 63.88410828r + r2 = 0 + 1280

Combine like terms: -1280 + 1280 = 0
0 + 63.88410828r + r2 = 0 + 1280
63.88410828r + r2 = 0 + 1280

Combine like terms: 0 + 1280 = 1280
63.88410828r + r2 = 1280

The r term is 63.88410828r.  Take half its coefficient (31.94205414).
Square it (1020.294823) and add it to both sides.

Add '1020.294823' to each side of the equation.
63.88410828r + 1020.294823 + r2 = 1280 + 1020.294823

Reorder the terms:
1020.294823 + 63.88410828r + r2 = 1280 + 1020.294823

Combine like terms: 1280 + 1020.294823 = 2300.294823
1020.294823 + 63.88410828r + r2 = 2300.294823

Factor a perfect square on the left side:
(r + 31.94205414)(r + 31.94205414) = 2300.294823

Calculate the square root of the right side: 47.961388877

Break this problem into two subproblems by setting 
(r + 31.94205414) equal to 47.961388877 and -47.961388877.

Subproblem 1
r + 31.94205414 = 47.961388877

Simplifying
r + 31.94205414 = 47.961388877

Reorder the terms:
31.94205414 + r = 47.961388877

Solving
31.94205414 + r = 47.961388877

Solving for variable 'r'.

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

Add '-31.94205414' to each side of the equation.
31.94205414 + -31.94205414 + r = 47.961388877 + -31.94205414

Combine like terms: 31.94205414 + -31.94205414 = 0.00000000
0.00000000 + r = 47.961388877 + -31.94205414
r = 47.961388877 + -31.94205414

Combine like terms: 47.961388877 + -31.94205414 = 16.019334737
r = 16.019334737

Simplifying
r = 16.019334737

Subproblem 2
r + 31.94205414 = -47.961388877

Simplifying
r + 31.94205414 = -47.961388877

Reorder the terms:
31.94205414 + r = -47.961388877

Solving
31.94205414 + r = -47.961388877

Solving for variable 'r'.

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

Add '-31.94205414' to each side of the equation.
31.94205414 + -31.94205414 + r = -47.961388877 + -31.94205414

Combine like terms: 31.94205414 + -31.94205414 = 0.00000000
0.00000000 + r = -47.961388877 + -31.94205414
r = -47.961388877 + -31.94205414

Combine like terms: -47.961388877 + -31.94205414 = -79.903443017
r = -79.903443017

Simplifying
r = -79.903443017

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {16.019334737, -79.903443017}