19540.6596=2*3.14r^2+2*3.14*r*111.6

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Solution for 19540.6596=2*3.14r^2+2*3.14*r*111.6 equation: 


Simplifying
19540.6596 = 2 * 3.14r2 + 2 * 3.14r * 111.6

Multiply 2 * 3.14
19540.6596 = 6.28r2 + 2 * 3.14r * 111.6

Reorder the terms for easier multiplication:
19540.6596 = 6.28r2 + 2 * 3.14 * 111.6r

Multiply 2 * 3.14
19540.6596 = 6.28r2 + 6.28 * 111.6r

Multiply 6.28 * 111.6
19540.6596 = 6.28r2 + 700.848r

Reorder the terms:
19540.6596 = 700.848r + 6.28r2

Solving
19540.6596 = 700.848r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
19540.6596 + -700.848r + -6.28r2 = 700.848r + -700.848r + 6.28r2 + -6.28r2

Combine like terms: 700.848r + -700.848r = 0.000
19540.6596 + -700.848r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
19540.6596 + -700.848r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
19540.6596 + -700.848r + -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'.
-3111.57 + 111.6r + r2 = 0

Move the constant term to the right:

Add '3111.57' to each side of the equation.
-3111.57 + 111.6r + 3111.57 + r2 = 0 + 3111.57

Reorder the terms:
-3111.57 + 3111.57 + 111.6r + r2 = 0 + 3111.57

Combine like terms: -3111.57 + 3111.57 = 0.00
0.00 + 111.6r + r2 = 0 + 3111.57
111.6r + r2 = 0 + 3111.57

Combine like terms: 0 + 3111.57 = 3111.57
111.6r + r2 = 3111.57

The r term is 111.6r.  Take half its coefficient (55.8).
Square it (3113.64) and add it to both sides.

Add '3113.64' to each side of the equation.
111.6r + 3113.64 + r2 = 3111.57 + 3113.64

Reorder the terms:
3113.64 + 111.6r + r2 = 3111.57 + 3113.64

Combine like terms: 3111.57 + 3113.64 = 6225.21
3113.64 + 111.6r + r2 = 6225.21

Factor a perfect square on the left side:
(r + 55.8)(r + 55.8) = 6225.21

Calculate the square root of the right side: 78.9

Break this problem into two subproblems by setting 
(r + 55.8) equal to 78.9 and -78.9.


Subproblem 1
r + 55.8 = 78.9

Simplifying
r + 55.8 = 78.9

Reorder the terms:
55.8 + r = 78.9

Solving
55.8 + r = 78.9

Solving for variable 'r'.

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

Add '-55.8' to each side of the equation.
55.8 + -55.8 + r = 78.9 + -55.8

Combine like terms: 55.8 + -55.8 = 0.0
0.0 + r = 78.9 + -55.8
r = 78.9 + -55.8

Combine like terms: 78.9 + -55.8 = 23.1
r = 23.1

Simplifying
r = 23.1


Subproblem 2
r + 55.8 = -78.9

Simplifying
r + 55.8 = -78.9

Reorder the terms:
55.8 + r = -78.9

Solving
55.8 + r = -78.9

Solving for variable 'r'.

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

Add '-55.8' to each side of the equation.
55.8 + -55.8 + r = -78.9 + -55.8

Combine like terms: 55.8 + -55.8 = 0.0
0.0 + r = -78.9 + -55.8
r = -78.9 + -55.8

Combine like terms: -78.9 + -55.8 = -134.7
r = -134.7

Simplifying
r = -134.7


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {23.1, -134.7}

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