16981.12=2*3.14*r^2+2*3.14*r*195

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Solution for 16981.12=2*3.14*r^2+2*3.14*r*195 equation: 


Simplifying
16981.12 = 2 * 3.14r2 + 2 * 3.14r * 195

Multiply 2 * 3.14
16981.12 = 6.28r2 + 2 * 3.14r * 195

Reorder the terms for easier multiplication:
16981.12 = 6.28r2 + 2 * 3.14 * 195r

Multiply 2 * 3.14
16981.12 = 6.28r2 + 6.28 * 195r

Multiply 6.28 * 195
16981.12 = 6.28r2 + 1224.6r

Reorder the terms:
16981.12 = 1224.6r + 6.28r2

Solving
16981.12 = 1224.6r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
16981.12 + -1224.6r + -6.28r2 = 1224.6r + -1224.6r + 6.28r2 + -6.28r2

Combine like terms: 1224.6r + -1224.6r = 0.0
16981.12 + -1224.6r + -6.28r2 = 0.0 + 6.28r2 + -6.28r2
16981.12 + -1224.6r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
16981.12 + -1224.6r + -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'.
-2704 + 195r + r2 = 0

Move the constant term to the right:

Add '2704' to each side of the equation.
-2704 + 195r + 2704 + r2 = 0 + 2704

Reorder the terms:
-2704 + 2704 + 195r + r2 = 0 + 2704

Combine like terms: -2704 + 2704 = 0
0 + 195r + r2 = 0 + 2704
195r + r2 = 0 + 2704

Combine like terms: 0 + 2704 = 2704
195r + r2 = 2704

The r term is 195r.  Take half its coefficient (97.5).
Square it (9506.25) and add it to both sides.

Add '9506.25' to each side of the equation.
195r + 9506.25 + r2 = 2704 + 9506.25

Reorder the terms:
9506.25 + 195r + r2 = 2704 + 9506.25

Combine like terms: 2704 + 9506.25 = 12210.25
9506.25 + 195r + r2 = 12210.25

Factor a perfect square on the left side:
(r + 97.5)(r + 97.5) = 12210.25

Calculate the square root of the right side: 110.5

Break this problem into two subproblems by setting 
(r + 97.5) equal to 110.5 and -110.5.


Subproblem 1
r + 97.5 = 110.5

Simplifying
r + 97.5 = 110.5

Reorder the terms:
97.5 + r = 110.5

Solving
97.5 + r = 110.5

Solving for variable 'r'.

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

Add '-97.5' to each side of the equation.
97.5 + -97.5 + r = 110.5 + -97.5

Combine like terms: 97.5 + -97.5 = 0.0
0.0 + r = 110.5 + -97.5
r = 110.5 + -97.5

Combine like terms: 110.5 + -97.5 = 13
r = 13

Simplifying
r = 13


Subproblem 2
r + 97.5 = -110.5

Simplifying
r + 97.5 = -110.5

Reorder the terms:
97.5 + r = -110.5

Solving
97.5 + r = -110.5

Solving for variable 'r'.

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

Add '-97.5' to each side of the equation.
97.5 + -97.5 + r = -110.5 + -97.5

Combine like terms: 97.5 + -97.5 = 0.0
0.0 + r = -110.5 + -97.5
r = -110.5 + -97.5

Combine like terms: -110.5 + -97.5 = -208
r = -208

Simplifying
r = -208


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {13, -208}

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