1616.786=2*3.14*r^2+2*3.14*r*9.5

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Solution for 1616.786=2*3.14*r^2+2*3.14*r*9.5 equation: 


Simplifying
1616.786 = 2 * 3.14r2 + 2 * 3.14r * 9.5

Multiply 2 * 3.14
1616.786 = 6.28r2 + 2 * 3.14r * 9.5

Reorder the terms for easier multiplication:
1616.786 = 6.28r2 + 2 * 3.14 * 9.5r

Multiply 2 * 3.14
1616.786 = 6.28r2 + 6.28 * 9.5r

Multiply 6.28 * 9.5
1616.786 = 6.28r2 + 59.66r

Reorder the terms:
1616.786 = 59.66r + 6.28r2

Solving
1616.786 = 59.66r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
1616.786 + -59.66r + -6.28r2 = 59.66r + -59.66r + 6.28r2 + -6.28r2

Combine like terms: 59.66r + -59.66r = 0.00
1616.786 + -59.66r + -6.28r2 = 0.00 + 6.28r2 + -6.28r2
1616.786 + -59.66r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
1616.786 + -59.66r + -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'.
-257.45 + 9.5r + r2 = 0

Move the constant term to the right:

Add '257.45' to each side of the equation.
-257.45 + 9.5r + 257.45 + r2 = 0 + 257.45

Reorder the terms:
-257.45 + 257.45 + 9.5r + r2 = 0 + 257.45

Combine like terms: -257.45 + 257.45 = 0.00
0.00 + 9.5r + r2 = 0 + 257.45
9.5r + r2 = 0 + 257.45

Combine like terms: 0 + 257.45 = 257.45
9.5r + r2 = 257.45

The r term is 9.5r.  Take half its coefficient (4.75).
Square it (22.5625) and add it to both sides.

Add '22.5625' to each side of the equation.
9.5r + 22.5625 + r2 = 257.45 + 22.5625

Reorder the terms:
22.5625 + 9.5r + r2 = 257.45 + 22.5625

Combine like terms: 257.45 + 22.5625 = 280.0125
22.5625 + 9.5r + r2 = 280.0125

Factor a perfect square on the left side:
(r + 4.75)(r + 4.75) = 280.0125

Calculate the square root of the right side: 16.733574035

Break this problem into two subproblems by setting 
(r + 4.75) equal to 16.733574035 and -16.733574035.


Subproblem 1
r + 4.75 = 16.733574035

Simplifying
r + 4.75 = 16.733574035

Reorder the terms:
4.75 + r = 16.733574035

Solving
4.75 + r = 16.733574035

Solving for variable 'r'.

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

Add '-4.75' to each side of the equation.
4.75 + -4.75 + r = 16.733574035 + -4.75

Combine like terms: 4.75 + -4.75 = 0.00
0.00 + r = 16.733574035 + -4.75
r = 16.733574035 + -4.75

Combine like terms: 16.733574035 + -4.75 = 11.983574035
r = 11.983574035

Simplifying
r = 11.983574035


Subproblem 2
r + 4.75 = -16.733574035

Simplifying
r + 4.75 = -16.733574035

Reorder the terms:
4.75 + r = -16.733574035

Solving
4.75 + r = -16.733574035

Solving for variable 'r'.

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

Add '-4.75' to each side of the equation.
4.75 + -4.75 + r = -16.733574035 + -4.75

Combine like terms: 4.75 + -4.75 = 0.00
0.00 + r = -16.733574035 + -4.75
r = -16.733574035 + -4.75

Combine like terms: -16.733574035 + -4.75 = -21.483574035
r = -21.483574035

Simplifying
r = -21.483574035


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {11.983574035, -21.483574035}

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