3318.1008=6.28r^2+6.28*r*36.5

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Solution for 3318.1008=6.28r^2+6.28*r*36.5 equation: 


Simplifying
3318.1008 = 6.28r2 + 6.28r * 36.5

Reorder the terms for easier multiplication:
3318.1008 = 6.28r2 + 6.28 * 36.5r

Multiply 6.28 * 36.5
3318.1008 = 6.28r2 + 229.22r

Reorder the terms:
3318.1008 = 229.22r + 6.28r2

Solving
3318.1008 = 229.22r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
3318.1008 + -229.22r + -6.28r2 = 229.22r + -229.22r + 6.28r2 + -6.28r2

Combine like terms: 229.22r + -229.22r = 0.00
3318.1008 + -229.22r + -6.28r2 = 0.00 + 6.28r2 + -6.28r2
3318.1008 + -229.22r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
3318.1008 + -229.22r + -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'.
-528.36 + 36.5r + r2 = 0

Move the constant term to the right:

Add '528.36' to each side of the equation.
-528.36 + 36.5r + 528.36 + r2 = 0 + 528.36

Reorder the terms:
-528.36 + 528.36 + 36.5r + r2 = 0 + 528.36

Combine like terms: -528.36 + 528.36 = 0.00
0.00 + 36.5r + r2 = 0 + 528.36
36.5r + r2 = 0 + 528.36

Combine like terms: 0 + 528.36 = 528.36
36.5r + r2 = 528.36

The r term is 36.5r.  Take half its coefficient (18.25).
Square it (333.0625) and add it to both sides.

Add '333.0625' to each side of the equation.
36.5r + 333.0625 + r2 = 528.36 + 333.0625

Reorder the terms:
333.0625 + 36.5r + r2 = 528.36 + 333.0625

Combine like terms: 528.36 + 333.0625 = 861.4225
333.0625 + 36.5r + r2 = 861.4225

Factor a perfect square on the left side:
(r + 18.25)(r + 18.25) = 861.4225

Calculate the square root of the right side: 29.35

Break this problem into two subproblems by setting 
(r + 18.25) equal to 29.35 and -29.35.


Subproblem 1
r + 18.25 = 29.35

Simplifying
r + 18.25 = 29.35

Reorder the terms:
18.25 + r = 29.35

Solving
18.25 + r = 29.35

Solving for variable 'r'.

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

Add '-18.25' to each side of the equation.
18.25 + -18.25 + r = 29.35 + -18.25

Combine like terms: 18.25 + -18.25 = 0.00
0.00 + r = 29.35 + -18.25
r = 29.35 + -18.25

Combine like terms: 29.35 + -18.25 = 11.1
r = 11.1

Simplifying
r = 11.1


Subproblem 2
r + 18.25 = -29.35

Simplifying
r + 18.25 = -29.35

Reorder the terms:
18.25 + r = -29.35

Solving
18.25 + r = -29.35

Solving for variable 'r'.

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

Add '-18.25' to each side of the equation.
18.25 + -18.25 + r = -29.35 + -18.25

Combine like terms: 18.25 + -18.25 = 0.00
0.00 + r = -29.35 + -18.25
r = -29.35 + -18.25

Combine like terms: -29.35 + -18.25 = -47.6
r = -47.6

Simplifying
r = -47.6


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {11.1, -47.6}

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