13886.964=2*3.14*r^2+2*3.14*r*98.1

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Solution for 13886.964=2*3.14*r^2+2*3.14*r*98.1 equation: 


Simplifying
13886.964 = 2 * 3.14r2 + 2 * 3.14r * 98.1

Multiply 2 * 3.14
13886.964 = 6.28r2 + 2 * 3.14r * 98.1

Reorder the terms for easier multiplication:
13886.964 = 6.28r2 + 2 * 3.14 * 98.1r

Multiply 2 * 3.14
13886.964 = 6.28r2 + 6.28 * 98.1r

Multiply 6.28 * 98.1
13886.964 = 6.28r2 + 616.068r

Reorder the terms:
13886.964 = 616.068r + 6.28r2

Solving
13886.964 = 616.068r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
13886.964 + -616.068r + -6.28r2 = 616.068r + -616.068r + 6.28r2 + -6.28r2

Combine like terms: 616.068r + -616.068r = 0.000
13886.964 + -616.068r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
13886.964 + -616.068r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
13886.964 + -616.068r + -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'.
-2211.3 + 98.1r + r2 = 0

Move the constant term to the right:

Add '2211.3' to each side of the equation.
-2211.3 + 98.1r + 2211.3 + r2 = 0 + 2211.3

Reorder the terms:
-2211.3 + 2211.3 + 98.1r + r2 = 0 + 2211.3

Combine like terms: -2211.3 + 2211.3 = 0.0
0.0 + 98.1r + r2 = 0 + 2211.3
98.1r + r2 = 0 + 2211.3

Combine like terms: 0 + 2211.3 = 2211.3
98.1r + r2 = 2211.3

The r term is 98.1r.  Take half its coefficient (49.05).
Square it (2405.9025) and add it to both sides.

Add '2405.9025' to each side of the equation.
98.1r + 2405.9025 + r2 = 2211.3 + 2405.9025

Reorder the terms:
2405.9025 + 98.1r + r2 = 2211.3 + 2405.9025

Combine like terms: 2211.3 + 2405.9025 = 4617.2025
2405.9025 + 98.1r + r2 = 4617.2025

Factor a perfect square on the left side:
(r + 49.05)(r + 49.05) = 4617.2025

Calculate the square root of the right side: 67.95

Break this problem into two subproblems by setting 
(r + 49.05) equal to 67.95 and -67.95.


Subproblem 1
r + 49.05 = 67.95

Simplifying
r + 49.05 = 67.95

Reorder the terms:
49.05 + r = 67.95

Solving
49.05 + r = 67.95

Solving for variable 'r'.

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

Add '-49.05' to each side of the equation.
49.05 + -49.05 + r = 67.95 + -49.05

Combine like terms: 49.05 + -49.05 = 0.00
0.00 + r = 67.95 + -49.05
r = 67.95 + -49.05

Combine like terms: 67.95 + -49.05 = 18.9
r = 18.9

Simplifying
r = 18.9


Subproblem 2
r + 49.05 = -67.95

Simplifying
r + 49.05 = -67.95

Reorder the terms:
49.05 + r = -67.95

Solving
49.05 + r = -67.95

Solving for variable 'r'.

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

Add '-49.05' to each side of the equation.
49.05 + -49.05 + r = -67.95 + -49.05

Combine like terms: 49.05 + -49.05 = 0.00
0.00 + r = -67.95 + -49.05
r = -67.95 + -49.05

Combine like terms: -67.95 + -49.05 = -117
r = -117

Simplifying
r = -117


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {18.9, -117}

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