14093.89=2*3.14*r^2+2*3.14*r*98.4

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Solution for 14093.89=2*3.14*r^2+2*3.14*r*98.4 equation: 


Simplifying
14093.89 = 2 * 3.14r2 + 2 * 3.14r * 98.4

Multiply 2 * 3.14
14093.89 = 6.28r2 + 2 * 3.14r * 98.4

Reorder the terms for easier multiplication:
14093.89 = 6.28r2 + 2 * 3.14 * 98.4r

Multiply 2 * 3.14
14093.89 = 6.28r2 + 6.28 * 98.4r

Multiply 6.28 * 98.4
14093.89 = 6.28r2 + 617.952r

Reorder the terms:
14093.89 = 617.952r + 6.28r2

Solving
14093.89 = 617.952r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
14093.89 + -617.952r + -6.28r2 = 617.952r + -617.952r + 6.28r2 + -6.28r2

Combine like terms: 617.952r + -617.952r = 0.000
14093.89 + -617.952r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
14093.89 + -617.952r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
14093.89 + -617.952r + -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'.
-2244.25 + 98.4r + r2 = 0

Move the constant term to the right:

Add '2244.25' to each side of the equation.
-2244.25 + 98.4r + 2244.25 + r2 = 0 + 2244.25

Reorder the terms:
-2244.25 + 2244.25 + 98.4r + r2 = 0 + 2244.25

Combine like terms: -2244.25 + 2244.25 = 0.00
0.00 + 98.4r + r2 = 0 + 2244.25
98.4r + r2 = 0 + 2244.25

Combine like terms: 0 + 2244.25 = 2244.25
98.4r + r2 = 2244.25

The r term is 98.4r.  Take half its coefficient (49.2).
Square it (2420.64) and add it to both sides.

Add '2420.64' to each side of the equation.
98.4r + 2420.64 + r2 = 2244.25 + 2420.64

Reorder the terms:
2420.64 + 98.4r + r2 = 2244.25 + 2420.64

Combine like terms: 2244.25 + 2420.64 = 4664.89
2420.64 + 98.4r + r2 = 4664.89

Factor a perfect square on the left side:
(r + 49.2)(r + 49.2) = 4664.89

Calculate the square root of the right side: 68.3

Break this problem into two subproblems by setting 
(r + 49.2) equal to 68.3 and -68.3.


Subproblem 1
r + 49.2 = 68.3

Simplifying
r + 49.2 = 68.3

Reorder the terms:
49.2 + r = 68.3

Solving
49.2 + r = 68.3

Solving for variable 'r'.

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

Add '-49.2' to each side of the equation.
49.2 + -49.2 + r = 68.3 + -49.2

Combine like terms: 49.2 + -49.2 = 0.0
0.0 + r = 68.3 + -49.2
r = 68.3 + -49.2

Combine like terms: 68.3 + -49.2 = 19.1
r = 19.1

Simplifying
r = 19.1


Subproblem 2
r + 49.2 = -68.3

Simplifying
r + 49.2 = -68.3

Reorder the terms:
49.2 + r = -68.3

Solving
49.2 + r = -68.3

Solving for variable 'r'.

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

Add '-49.2' to each side of the equation.
49.2 + -49.2 + r = -68.3 + -49.2

Combine like terms: 49.2 + -49.2 = 0.0
0.0 + r = -68.3 + -49.2
r = -68.3 + -49.2

Combine like terms: -68.3 + -49.2 = -117.5
r = -117.5

Simplifying
r = -117.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {19.1, -117.5}

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