3040.2736=2*3.14r^2+2*3.14*r*93.9

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Solution for 3040.2736=2*3.14r^2+2*3.14*r*93.9 equation: 


Simplifying
3040.2736 = 2 * 3.14r2 + 2 * 3.14r * 93.9

Multiply 2 * 3.14
3040.2736 = 6.28r2 + 2 * 3.14r * 93.9

Reorder the terms for easier multiplication:
3040.2736 = 6.28r2 + 2 * 3.14 * 93.9r

Multiply 2 * 3.14
3040.2736 = 6.28r2 + 6.28 * 93.9r

Multiply 6.28 * 93.9
3040.2736 = 6.28r2 + 589.692r

Reorder the terms:
3040.2736 = 589.692r + 6.28r2

Solving
3040.2736 = 589.692r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
3040.2736 + -589.692r + -6.28r2 = 589.692r + -589.692r + 6.28r2 + -6.28r2

Combine like terms: 589.692r + -589.692r = 0.000
3040.2736 + -589.692r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
3040.2736 + -589.692r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
3040.2736 + -589.692r + -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'.
-484.12 + 93.9r + r2 = 0

Move the constant term to the right:

Add '484.12' to each side of the equation.
-484.12 + 93.9r + 484.12 + r2 = 0 + 484.12

Reorder the terms:
-484.12 + 484.12 + 93.9r + r2 = 0 + 484.12

Combine like terms: -484.12 + 484.12 = 0.00
0.00 + 93.9r + r2 = 0 + 484.12
93.9r + r2 = 0 + 484.12

Combine like terms: 0 + 484.12 = 484.12
93.9r + r2 = 484.12

The r term is 93.9r.  Take half its coefficient (46.95).
Square it (2204.3025) and add it to both sides.

Add '2204.3025' to each side of the equation.
93.9r + 2204.3025 + r2 = 484.12 + 2204.3025

Reorder the terms:
2204.3025 + 93.9r + r2 = 484.12 + 2204.3025

Combine like terms: 484.12 + 2204.3025 = 2688.4225
2204.3025 + 93.9r + r2 = 2688.4225

Factor a perfect square on the left side:
(r + 46.95)(r + 46.95) = 2688.4225

Calculate the square root of the right side: 51.85

Break this problem into two subproblems by setting 
(r + 46.95) equal to 51.85 and -51.85.


Subproblem 1
r + 46.95 = 51.85

Simplifying
r + 46.95 = 51.85

Reorder the terms:
46.95 + r = 51.85

Solving
46.95 + r = 51.85

Solving for variable 'r'.

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

Add '-46.95' to each side of the equation.
46.95 + -46.95 + r = 51.85 + -46.95

Combine like terms: 46.95 + -46.95 = 0.00
0.00 + r = 51.85 + -46.95
r = 51.85 + -46.95

Combine like terms: 51.85 + -46.95 = 4.9
r = 4.9

Simplifying
r = 4.9


Subproblem 2
r + 46.95 = -51.85

Simplifying
r + 46.95 = -51.85

Reorder the terms:
46.95 + r = -51.85

Solving
46.95 + r = -51.85

Solving for variable 'r'.

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

Add '-46.95' to each side of the equation.
46.95 + -46.95 + r = -51.85 + -46.95

Combine like terms: 46.95 + -46.95 = 0.00
0.00 + r = -51.85 + -46.95
r = -51.85 + -46.95

Combine like terms: -51.85 + -46.95 = -98.8
r = -98.8

Simplifying
r = -98.8


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {4.9, -98.8}

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