2442.7316=2*3.14*r^2+2*3.14*30.4r

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Solution for 2442.7316=2*3.14*r^2+2*3.14*30.4r equation: 


Simplifying
2442.7316 = 2 * 3.14r2 + 2 * 3.14 * 30.4r

Multiply 2 * 3.14
2442.7316 = 6.28r2 + 2 * 3.14 * 30.4r

Multiply 2 * 3.14
2442.7316 = 6.28r2 + 6.28 * 30.4r

Multiply 6.28 * 30.4
2442.7316 = 6.28r2 + 190.912r

Reorder the terms:
2442.7316 = 190.912r + 6.28r2

Solving
2442.7316 = 190.912r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
2442.7316 + -190.912r + -6.28r2 = 190.912r + -190.912r + 6.28r2 + -6.28r2

Combine like terms: 190.912r + -190.912r = 0.000
2442.7316 + -190.912r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
2442.7316 + -190.912r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
2442.7316 + -190.912r + -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'.
-388.97 + 30.4r + r2 = 0

Move the constant term to the right:

Add '388.97' to each side of the equation.
-388.97 + 30.4r + 388.97 + r2 = 0 + 388.97

Reorder the terms:
-388.97 + 388.97 + 30.4r + r2 = 0 + 388.97

Combine like terms: -388.97 + 388.97 = 0.00
0.00 + 30.4r + r2 = 0 + 388.97
30.4r + r2 = 0 + 388.97

Combine like terms: 0 + 388.97 = 388.97
30.4r + r2 = 388.97

The r term is 30.4r.  Take half its coefficient (15.2).
Square it (231.04) and add it to both sides.

Add '231.04' to each side of the equation.
30.4r + 231.04 + r2 = 388.97 + 231.04

Reorder the terms:
231.04 + 30.4r + r2 = 388.97 + 231.04

Combine like terms: 388.97 + 231.04 = 620.01
231.04 + 30.4r + r2 = 620.01

Factor a perfect square on the left side:
(r + 15.2)(r + 15.2) = 620.01

Calculate the square root of the right side: 24.9

Break this problem into two subproblems by setting 
(r + 15.2) equal to 24.9 and -24.9.


Subproblem 1
r + 15.2 = 24.9

Simplifying
r + 15.2 = 24.9

Reorder the terms:
15.2 + r = 24.9

Solving
15.2 + r = 24.9

Solving for variable 'r'.

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

Add '-15.2' to each side of the equation.
15.2 + -15.2 + r = 24.9 + -15.2

Combine like terms: 15.2 + -15.2 = 0.0
0.0 + r = 24.9 + -15.2
r = 24.9 + -15.2

Combine like terms: 24.9 + -15.2 = 9.7
r = 9.7

Simplifying
r = 9.7


Subproblem 2
r + 15.2 = -24.9

Simplifying
r + 15.2 = -24.9

Reorder the terms:
15.2 + r = -24.9

Solving
15.2 + r = -24.9

Solving for variable 'r'.

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

Add '-15.2' to each side of the equation.
15.2 + -15.2 + r = -24.9 + -15.2

Combine like terms: 15.2 + -15.2 = 0.0
0.0 + r = -24.9 + -15.2
r = -24.9 + -15.2

Combine like terms: -24.9 + -15.2 = -40.1
r = -40.1

Simplifying
r = -40.1


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {9.7, -40.1}

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