14828.65=2*3.14*r^2+2*3.14r

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Solution for 14828.65=2*3.14*r^2+2*3.14r equation: 


Simplifying
14828.65 = 2 * 3.14r2 + 2 * 3.14r

Multiply 2 * 3.14
14828.65 = 6.28r2 + 2 * 3.14r

Multiply 2 * 3.14
14828.65 = 6.28r2 + 6.28r

Reorder the terms:
14828.65 = 6.28r + 6.28r2

Solving
14828.65 = 6.28r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
14828.65 + -6.28r + -6.28r2 = 6.28r + -6.28r + 6.28r2 + -6.28r2

Combine like terms: 6.28r + -6.28r = 0.00
14828.65 + -6.28r + -6.28r2 = 0.00 + 6.28r2 + -6.28r2
14828.65 + -6.28r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
14828.65 + -6.28r + -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'.
-2361.25 + r + r2 = 0

Move the constant term to the right:

Add '2361.25' to each side of the equation.
-2361.25 + r + 2361.25 + r2 = 0 + 2361.25

Reorder the terms:
-2361.25 + 2361.25 + r + r2 = 0 + 2361.25

Combine like terms: -2361.25 + 2361.25 = 0.00
0.00 + r + r2 = 0 + 2361.25
r + r2 = 0 + 2361.25

Combine like terms: 0 + 2361.25 = 2361.25
r + r2 = 2361.25

The r term is r.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + r2 = 2361.25 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + r2 = 2361.25 + 0.25

Combine like terms: 2361.25 + 0.25 = 2361.5
1.25 + r2 = 2361.5

Factor a perfect square on the left side:
(r + 0.5)(r + 0.5) = 2361.5

Calculate the square root of the right side: 48.595267259

Break this problem into two subproblems by setting 
(r + 0.5) equal to 48.595267259 and -48.595267259.


Subproblem 1
r + 0.5 = 48.595267259

Simplifying
r + 0.5 = 48.595267259

Reorder the terms:
0.5 + r = 48.595267259

Solving
0.5 + r = 48.595267259

Solving for variable 'r'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + r = 48.595267259 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = 48.595267259 + -0.5
r = 48.595267259 + -0.5

Combine like terms: 48.595267259 + -0.5 = 48.095267259
r = 48.095267259

Simplifying
r = 48.095267259


Subproblem 2
r + 0.5 = -48.595267259

Simplifying
r + 0.5 = -48.595267259

Reorder the terms:
0.5 + r = -48.595267259

Solving
0.5 + r = -48.595267259

Solving for variable 'r'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + r = -48.595267259 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = -48.595267259 + -0.5
r = -48.595267259 + -0.5

Combine like terms: -48.595267259 + -0.5 = -49.095267259
r = -49.095267259

Simplifying
r = -49.095267259


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {48.095267259, -49.095267259}

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