285.9912=2*3.14r^2+2*3.14*r*5.3

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Solution for 285.9912=2*3.14r^2+2*3.14*r*5.3 equation: 


Simplifying
285.9912 = 2 * 3.14r2 + 2 * 3.14r * 5.3

Multiply 2 * 3.14
285.9912 = 6.28r2 + 2 * 3.14r * 5.3

Reorder the terms for easier multiplication:
285.9912 = 6.28r2 + 2 * 3.14 * 5.3r

Multiply 2 * 3.14
285.9912 = 6.28r2 + 6.28 * 5.3r

Multiply 6.28 * 5.3
285.9912 = 6.28r2 + 33.284r

Reorder the terms:
285.9912 = 33.284r + 6.28r2

Solving
285.9912 = 33.284r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
285.9912 + -33.284r + -6.28r2 = 33.284r + -33.284r + 6.28r2 + -6.28r2

Combine like terms: 33.284r + -33.284r = 0.000
285.9912 + -33.284r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
285.9912 + -33.284r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
285.9912 + -33.284r + -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'.
-45.54 + 5.3r + r2 = 0

Move the constant term to the right:

Add '45.54' to each side of the equation.
-45.54 + 5.3r + 45.54 + r2 = 0 + 45.54

Reorder the terms:
-45.54 + 45.54 + 5.3r + r2 = 0 + 45.54

Combine like terms: -45.54 + 45.54 = 0.00
0.00 + 5.3r + r2 = 0 + 45.54
5.3r + r2 = 0 + 45.54

Combine like terms: 0 + 45.54 = 45.54
5.3r + r2 = 45.54

The r term is 5.3r.  Take half its coefficient (2.65).
Square it (7.0225) and add it to both sides.

Add '7.0225' to each side of the equation.
5.3r + 7.0225 + r2 = 45.54 + 7.0225

Reorder the terms:
7.0225 + 5.3r + r2 = 45.54 + 7.0225

Combine like terms: 45.54 + 7.0225 = 52.5625
7.0225 + 5.3r + r2 = 52.5625

Factor a perfect square on the left side:
(r + 2.65)(r + 2.65) = 52.5625

Calculate the square root of the right side: 7.25

Break this problem into two subproblems by setting 
(r + 2.65) equal to 7.25 and -7.25.


Subproblem 1
r + 2.65 = 7.25

Simplifying
r + 2.65 = 7.25

Reorder the terms:
2.65 + r = 7.25

Solving
2.65 + r = 7.25

Solving for variable 'r'.

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

Add '-2.65' to each side of the equation.
2.65 + -2.65 + r = 7.25 + -2.65

Combine like terms: 2.65 + -2.65 = 0.00
0.00 + r = 7.25 + -2.65
r = 7.25 + -2.65

Combine like terms: 7.25 + -2.65 = 4.6
r = 4.6

Simplifying
r = 4.6


Subproblem 2
r + 2.65 = -7.25

Simplifying
r + 2.65 = -7.25

Reorder the terms:
2.65 + r = -7.25

Solving
2.65 + r = -7.25

Solving for variable 'r'.

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

Add '-2.65' to each side of the equation.
2.65 + -2.65 + r = -7.25 + -2.65

Combine like terms: 2.65 + -2.65 = 0.00
0.00 + r = -7.25 + -2.65
r = -7.25 + -2.65

Combine like terms: -7.25 + -2.65 = -9.9
r = -9.9

Simplifying
r = -9.9


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {4.6, -9.9}

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