181.2408=2*3.14r^2+2*3.14r*8.5

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Solution for 181.2408=2*3.14r^2+2*3.14r*8.5 equation: 


Simplifying
181.2408 = 2 * 3.14r2 + 2 * 3.14r * 8.5

Multiply 2 * 3.14
181.2408 = 6.28r2 + 2 * 3.14r * 8.5

Reorder the terms for easier multiplication:
181.2408 = 6.28r2 + 2 * 3.14 * 8.5r

Multiply 2 * 3.14
181.2408 = 6.28r2 + 6.28 * 8.5r

Multiply 6.28 * 8.5
181.2408 = 6.28r2 + 53.38r

Reorder the terms:
181.2408 = 53.38r + 6.28r2

Solving
181.2408 = 53.38r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
181.2408 + -53.38r + -6.28r2 = 53.38r + -53.38r + 6.28r2 + -6.28r2

Combine like terms: 53.38r + -53.38r = 0.00
181.2408 + -53.38r + -6.28r2 = 0.00 + 6.28r2 + -6.28r2
181.2408 + -53.38r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
181.2408 + -53.38r + -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'.
-28.86 + 8.5r + r2 = 0

Move the constant term to the right:

Add '28.86' to each side of the equation.
-28.86 + 8.5r + 28.86 + r2 = 0 + 28.86

Reorder the terms:
-28.86 + 28.86 + 8.5r + r2 = 0 + 28.86

Combine like terms: -28.86 + 28.86 = 0.00
0.00 + 8.5r + r2 = 0 + 28.86
8.5r + r2 = 0 + 28.86

Combine like terms: 0 + 28.86 = 28.86
8.5r + r2 = 28.86

The r term is 8.5r.  Take half its coefficient (4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
8.5r + 18.0625 + r2 = 28.86 + 18.0625

Reorder the terms:
18.0625 + 8.5r + r2 = 28.86 + 18.0625

Combine like terms: 28.86 + 18.0625 = 46.9225
18.0625 + 8.5r + r2 = 46.9225

Factor a perfect square on the left side:
(r + 4.25)(r + 4.25) = 46.9225

Calculate the square root of the right side: 6.85

Break this problem into two subproblems by setting 
(r + 4.25) equal to 6.85 and -6.85.


Subproblem 1
r + 4.25 = 6.85

Simplifying
r + 4.25 = 6.85

Reorder the terms:
4.25 + r = 6.85

Solving
4.25 + r = 6.85

Solving for variable 'r'.

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

Add '-4.25' to each side of the equation.
4.25 + -4.25 + r = 6.85 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + r = 6.85 + -4.25
r = 6.85 + -4.25

Combine like terms: 6.85 + -4.25 = 2.6
r = 2.6

Simplifying
r = 2.6


Subproblem 2
r + 4.25 = -6.85

Simplifying
r + 4.25 = -6.85

Reorder the terms:
4.25 + r = -6.85

Solving
4.25 + r = -6.85

Solving for variable 'r'.

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

Add '-4.25' to each side of the equation.
4.25 + -4.25 + r = -6.85 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + r = -6.85 + -4.25
r = -6.85 + -4.25

Combine like terms: -6.85 + -4.25 = -11.1
r = -11.1

Simplifying
r = -11.1


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {2.6, -11.1}

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