3087.3736=2(3.14)r^2+2(3.14)r*99.9

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Solution for 3087.3736=2(3.14)r^2+2(3.14)r*99.9 equation: 


Simplifying
3087.3736 = 2(3.14) * r2 + 2(3.14) * r * 99.9

Multiply 2 * 3.14
3087.3736 = 6.28r2 + 2(3.14) * r * 99.9

Reorder the terms for easier multiplication:
3087.3736 = 6.28r2 + 2 * 3.14 * 99.9r

Multiply 2 * 3.14
3087.3736 = 6.28r2 + 6.28 * 99.9r

Multiply 6.28 * 99.9
3087.3736 = 6.28r2 + 627.372r

Reorder the terms:
3087.3736 = 627.372r + 6.28r2

Solving
3087.3736 = 627.372r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
3087.3736 + -627.372r + -6.28r2 = 627.372r + -627.372r + 6.28r2 + -6.28r2

Combine like terms: 627.372r + -627.372r = 0.000
3087.3736 + -627.372r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
3087.3736 + -627.372r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
3087.3736 + -627.372r + -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'.
-491.62 + 99.9r + r2 = 0

Move the constant term to the right:

Add '491.62' to each side of the equation.
-491.62 + 99.9r + 491.62 + r2 = 0 + 491.62

Reorder the terms:
-491.62 + 491.62 + 99.9r + r2 = 0 + 491.62

Combine like terms: -491.62 + 491.62 = 0.00
0.00 + 99.9r + r2 = 0 + 491.62
99.9r + r2 = 0 + 491.62

Combine like terms: 0 + 491.62 = 491.62
99.9r + r2 = 491.62

The r term is 99.9r.  Take half its coefficient (49.95).
Square it (2495.0025) and add it to both sides.

Add '2495.0025' to each side of the equation.
99.9r + 2495.0025 + r2 = 491.62 + 2495.0025

Reorder the terms:
2495.0025 + 99.9r + r2 = 491.62 + 2495.0025

Combine like terms: 491.62 + 2495.0025 = 2986.6225
2495.0025 + 99.9r + r2 = 2986.6225

Factor a perfect square on the left side:
(r + 49.95)(r + 49.95) = 2986.6225

Calculate the square root of the right side: 54.65

Break this problem into two subproblems by setting 
(r + 49.95) equal to 54.65 and -54.65.


Subproblem 1
r + 49.95 = 54.65

Simplifying
r + 49.95 = 54.65

Reorder the terms:
49.95 + r = 54.65

Solving
49.95 + r = 54.65

Solving for variable 'r'.

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

Add '-49.95' to each side of the equation.
49.95 + -49.95 + r = 54.65 + -49.95

Combine like terms: 49.95 + -49.95 = 0.00
0.00 + r = 54.65 + -49.95
r = 54.65 + -49.95

Combine like terms: 54.65 + -49.95 = 4.7
r = 4.7

Simplifying
r = 4.7


Subproblem 2
r + 49.95 = -54.65

Simplifying
r + 49.95 = -54.65

Reorder the terms:
49.95 + r = -54.65

Solving
49.95 + r = -54.65

Solving for variable 'r'.

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

Add '-49.95' to each side of the equation.
49.95 + -49.95 + r = -54.65 + -49.95

Combine like terms: 49.95 + -49.95 = 0.00
0.00 + r = -54.65 + -49.95
r = -54.65 + -49.95

Combine like terms: -54.65 + -49.95 = -104.6
r = -104.6

Simplifying
r = -104.6


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {4.7, -104.6}

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