3668.8388=2*3.14*r^2+2*3.14*r*40.4

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Solution for 3668.8388=2*3.14*r^2+2*3.14*r*40.4 equation: 


Simplifying
3668.8388 = 2 * 3.14r2 + 2 * 3.14r * 40.4

Multiply 2 * 3.14
3668.8388 = 6.28r2 + 2 * 3.14r * 40.4

Reorder the terms for easier multiplication:
3668.8388 = 6.28r2 + 2 * 3.14 * 40.4r

Multiply 2 * 3.14
3668.8388 = 6.28r2 + 6.28 * 40.4r

Multiply 6.28 * 40.4
3668.8388 = 6.28r2 + 253.712r

Reorder the terms:
3668.8388 = 253.712r + 6.28r2

Solving
3668.8388 = 253.712r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
3668.8388 + -253.712r + -6.28r2 = 253.712r + -253.712r + 6.28r2 + -6.28r2

Combine like terms: 253.712r + -253.712r = 0.000
3668.8388 + -253.712r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
3668.8388 + -253.712r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
3668.8388 + -253.712r + -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'.
-584.21 + 40.4r + r2 = 0

Move the constant term to the right:

Add '584.21' to each side of the equation.
-584.21 + 40.4r + 584.21 + r2 = 0 + 584.21

Reorder the terms:
-584.21 + 584.21 + 40.4r + r2 = 0 + 584.21

Combine like terms: -584.21 + 584.21 = 0.00
0.00 + 40.4r + r2 = 0 + 584.21
40.4r + r2 = 0 + 584.21

Combine like terms: 0 + 584.21 = 584.21
40.4r + r2 = 584.21

The r term is 40.4r.  Take half its coefficient (20.2).
Square it (408.04) and add it to both sides.

Add '408.04' to each side of the equation.
40.4r + 408.04 + r2 = 584.21 + 408.04

Reorder the terms:
408.04 + 40.4r + r2 = 584.21 + 408.04

Combine like terms: 584.21 + 408.04 = 992.25
408.04 + 40.4r + r2 = 992.25

Factor a perfect square on the left side:
(r + 20.2)(r + 20.2) = 992.25

Calculate the square root of the right side: 31.5

Break this problem into two subproblems by setting 
(r + 20.2) equal to 31.5 and -31.5.


Subproblem 1
r + 20.2 = 31.5

Simplifying
r + 20.2 = 31.5

Reorder the terms:
20.2 + r = 31.5

Solving
20.2 + r = 31.5

Solving for variable 'r'.

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

Add '-20.2' to each side of the equation.
20.2 + -20.2 + r = 31.5 + -20.2

Combine like terms: 20.2 + -20.2 = 0.0
0.0 + r = 31.5 + -20.2
r = 31.5 + -20.2

Combine like terms: 31.5 + -20.2 = 11.3
r = 11.3

Simplifying
r = 11.3


Subproblem 2
r + 20.2 = -31.5

Simplifying
r + 20.2 = -31.5

Reorder the terms:
20.2 + r = -31.5

Solving
20.2 + r = -31.5

Solving for variable 'r'.

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

Add '-20.2' to each side of the equation.
20.2 + -20.2 + r = -31.5 + -20.2

Combine like terms: 20.2 + -20.2 = 0.0
0.0 + r = -31.5 + -20.2
r = -31.5 + -20.2

Combine like terms: -31.5 + -20.2 = -51.7
r = -51.7

Simplifying
r = -51.7


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {11.3, -51.7}

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