5651.8116=6.28*r^2+349.168*r

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Solution for 5651.8116=6.28*r^2+349.168*r equation: 


Simplifying
5651.8116 = 6.28r2 + 349.168r

Reorder the terms:
5651.8116 = 349.168r + 6.28r2

Solving
5651.8116 = 349.168r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
5651.8116 + -349.168r + -6.28r2 = 349.168r + -349.168r + 6.28r2 + -6.28r2

Combine like terms: 349.168r + -349.168r = 0.000
5651.8116 + -349.168r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
5651.8116 + -349.168r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
5651.8116 + -349.168r + -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'.
-899.97 + 55.6r + r2 = 0

Move the constant term to the right:

Add '899.97' to each side of the equation.
-899.97 + 55.6r + 899.97 + r2 = 0 + 899.97

Reorder the terms:
-899.97 + 899.97 + 55.6r + r2 = 0 + 899.97

Combine like terms: -899.97 + 899.97 = 0.00
0.00 + 55.6r + r2 = 0 + 899.97
55.6r + r2 = 0 + 899.97

Combine like terms: 0 + 899.97 = 899.97
55.6r + r2 = 899.97

The r term is 55.6r.  Take half its coefficient (27.8).
Square it (772.84) and add it to both sides.

Add '772.84' to each side of the equation.
55.6r + 772.84 + r2 = 899.97 + 772.84

Reorder the terms:
772.84 + 55.6r + r2 = 899.97 + 772.84

Combine like terms: 899.97 + 772.84 = 1672.81
772.84 + 55.6r + r2 = 1672.81

Factor a perfect square on the left side:
(r + 27.8)(r + 27.8) = 1672.81

Calculate the square root of the right side: 40.9

Break this problem into two subproblems by setting 
(r + 27.8) equal to 40.9 and -40.9.


Subproblem 1
r + 27.8 = 40.9

Simplifying
r + 27.8 = 40.9

Reorder the terms:
27.8 + r = 40.9

Solving
27.8 + r = 40.9

Solving for variable 'r'.

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

Add '-27.8' to each side of the equation.
27.8 + -27.8 + r = 40.9 + -27.8

Combine like terms: 27.8 + -27.8 = 0.0
0.0 + r = 40.9 + -27.8
r = 40.9 + -27.8

Combine like terms: 40.9 + -27.8 = 13.1
r = 13.1

Simplifying
r = 13.1


Subproblem 2
r + 27.8 = -40.9

Simplifying
r + 27.8 = -40.9

Reorder the terms:
27.8 + r = -40.9

Solving
27.8 + r = -40.9

Solving for variable 'r'.

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

Add '-27.8' to each side of the equation.
27.8 + -27.8 + r = -40.9 + -27.8

Combine like terms: 27.8 + -27.8 = 0.0
0.0 + r = -40.9 + -27.8
r = -40.9 + -27.8

Combine like terms: -40.9 + -27.8 = -68.7
r = -68.7

Simplifying
r = -68.7


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {13.1, -68.7}

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