550.8816=2*3.14*r^2+2*3.14*r*16.1

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Solution for 550.8816=2*3.14*r^2+2*3.14*r*16.1 equation: 


Simplifying
550.8816 = 2 * 3.14r2 + 2 * 3.14r * 16.1

Multiply 2 * 3.14
550.8816 = 6.28r2 + 2 * 3.14r * 16.1

Reorder the terms for easier multiplication:
550.8816 = 6.28r2 + 2 * 3.14 * 16.1r

Multiply 2 * 3.14
550.8816 = 6.28r2 + 6.28 * 16.1r

Multiply 6.28 * 16.1
550.8816 = 6.28r2 + 101.108r

Reorder the terms:
550.8816 = 101.108r + 6.28r2

Solving
550.8816 = 101.108r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
550.8816 + -101.108r + -6.28r2 = 101.108r + -101.108r + 6.28r2 + -6.28r2

Combine like terms: 101.108r + -101.108r = 0.000
550.8816 + -101.108r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
550.8816 + -101.108r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
550.8816 + -101.108r + -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'.
-87.72 + 16.1r + r2 = 0

Move the constant term to the right:

Add '87.72' to each side of the equation.
-87.72 + 16.1r + 87.72 + r2 = 0 + 87.72

Reorder the terms:
-87.72 + 87.72 + 16.1r + r2 = 0 + 87.72

Combine like terms: -87.72 + 87.72 = 0.00
0.00 + 16.1r + r2 = 0 + 87.72
16.1r + r2 = 0 + 87.72

Combine like terms: 0 + 87.72 = 87.72
16.1r + r2 = 87.72

The r term is 16.1r.  Take half its coefficient (8.05).
Square it (64.8025) and add it to both sides.

Add '64.8025' to each side of the equation.
16.1r + 64.8025 + r2 = 87.72 + 64.8025

Reorder the terms:
64.8025 + 16.1r + r2 = 87.72 + 64.8025

Combine like terms: 87.72 + 64.8025 = 152.5225
64.8025 + 16.1r + r2 = 152.5225

Factor a perfect square on the left side:
(r + 8.05)(r + 8.05) = 152.5225

Calculate the square root of the right side: 12.35

Break this problem into two subproblems by setting 
(r + 8.05) equal to 12.35 and -12.35.


Subproblem 1
r + 8.05 = 12.35

Simplifying
r + 8.05 = 12.35

Reorder the terms:
8.05 + r = 12.35

Solving
8.05 + r = 12.35

Solving for variable 'r'.

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

Add '-8.05' to each side of the equation.
8.05 + -8.05 + r = 12.35 + -8.05

Combine like terms: 8.05 + -8.05 = 0.00
0.00 + r = 12.35 + -8.05
r = 12.35 + -8.05

Combine like terms: 12.35 + -8.05 = 4.3
r = 4.3

Simplifying
r = 4.3


Subproblem 2
r + 8.05 = -12.35

Simplifying
r + 8.05 = -12.35

Reorder the terms:
8.05 + r = -12.35

Solving
8.05 + r = -12.35

Solving for variable 'r'.

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

Add '-8.05' to each side of the equation.
8.05 + -8.05 + r = -12.35 + -8.05

Combine like terms: 8.05 + -8.05 = 0.00
0.00 + r = -12.35 + -8.05
r = -12.35 + -8.05

Combine like terms: -12.35 + -8.05 = -20.4
r = -20.4

Simplifying
r = -20.4


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {4.3, -20.4}

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