7009.2336=6.28r^2+6.28r(64.6)

Solution for 7009.2336=6.28r^2+6.28r(64.6) equation:

Simplifying
7009.2336 = 6.28r2 + 6.28r(64.6)

Reorder the terms for easier multiplication:
7009.2336 = 6.28r2 + 6.28 * 64.6r

Multiply 6.28 * 64.6
7009.2336 = 6.28r2 + 405.688r

Reorder the terms:
7009.2336 = 405.688r + 6.28r2

Solving
7009.2336 = 405.688r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
7009.2336 + -405.688r + -6.28r2 = 405.688r + -405.688r + 6.28r2 + -6.28r2

Combine like terms: 405.688r + -405.688r = 0.000
7009.2336 + -405.688r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
7009.2336 + -405.688r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
7009.2336 + -405.688r + -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'.
-1116.12 + 64.6r + r2 = 0

Move the constant term to the right:

Add '1116.12' to each side of the equation.
-1116.12 + 64.6r + 1116.12 + r2 = 0 + 1116.12

Reorder the terms:
-1116.12 + 1116.12 + 64.6r + r2 = 0 + 1116.12

Combine like terms: -1116.12 + 1116.12 = 0.00
0.00 + 64.6r + r2 = 0 + 1116.12
64.6r + r2 = 0 + 1116.12

Combine like terms: 0 + 1116.12 = 1116.12
64.6r + r2 = 1116.12

The r term is 64.6r.  Take half its coefficient (32.3).
Square it (1043.29) and add it to both sides.

Add '1043.29' to each side of the equation.
64.6r + 1043.29 + r2 = 1116.12 + 1043.29

Reorder the terms:
1043.29 + 64.6r + r2 = 1116.12 + 1043.29

Combine like terms: 1116.12 + 1043.29 = 2159.41
1043.29 + 64.6r + r2 = 2159.41

Factor a perfect square on the left side:
(r + 32.3)(r + 32.3) = 2159.41

Calculate the square root of the right side: 46.469452332

Break this problem into two subproblems by setting 
(r + 32.3) equal to 46.469452332 and -46.469452332.

Subproblem 1
r + 32.3 = 46.469452332

Simplifying
r + 32.3 = 46.469452332

Reorder the terms:
32.3 + r = 46.469452332

Solving
32.3 + r = 46.469452332

Solving for variable 'r'.

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

Add '-32.3' to each side of the equation.
32.3 + -32.3 + r = 46.469452332 + -32.3

Combine like terms: 32.3 + -32.3 = 0.0
0.0 + r = 46.469452332 + -32.3
r = 46.469452332 + -32.3

Combine like terms: 46.469452332 + -32.3 = 14.169452332
r = 14.169452332

Simplifying
r = 14.169452332

Subproblem 2
r + 32.3 = -46.469452332

Simplifying
r + 32.3 = -46.469452332

Reorder the terms:
32.3 + r = -46.469452332

Solving
32.3 + r = -46.469452332

Solving for variable 'r'.

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

Add '-32.3' to each side of the equation.
32.3 + -32.3 + r = -46.469452332 + -32.3

Combine like terms: 32.3 + -32.3 = 0.0
0.0 + r = -46.469452332 + -32.3
r = -46.469452332 + -32.3

Combine like terms: -46.469452332 + -32.3 = -78.769452332
r = -78.769452332

Simplifying
r = -78.769452332

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {14.169452332, -78.769452332}