242.0584=2(3.14*r^2)+2*3.14*r*38.3

Solution for 242.0584=2(3.14*r^2)+2*3.14*r*38.3 equation:

Simplifying
242.0584 = 2(3.14r2) + 2 * 3.14r * 38.3

Remove parenthesis around (3.14r2)
242.0584 = 2 * 3.14r2 + 2 * 3.14r * 38.3

Multiply 2 * 3.14
242.0584 = 6.28r2 + 2 * 3.14r * 38.3

Reorder the terms for easier multiplication:
242.0584 = 6.28r2 + 2 * 3.14 * 38.3r

Multiply 2 * 3.14
242.0584 = 6.28r2 + 6.28 * 38.3r

Multiply 6.28 * 38.3
242.0584 = 6.28r2 + 240.524r

Reorder the terms:
242.0584 = 240.524r + 6.28r2

Solving
242.0584 = 240.524r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
242.0584 + -240.524r + -6.28r2 = 240.524r + -240.524r + 6.28r2 + -6.28r2

Combine like terms: 240.524r + -240.524r = 0.000
242.0584 + -240.524r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
242.0584 + -240.524r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
242.0584 + -240.524r + -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'.
-38.54433121 + 38.3r + r2 = 0

Move the constant term to the right:

Add '38.54433121' to each side of the equation.
-38.54433121 + 38.3r + 38.54433121 + r2 = 0 + 38.54433121

Reorder the terms:
-38.54433121 + 38.54433121 + 38.3r + r2 = 0 + 38.54433121

Combine like terms: -38.54433121 + 38.54433121 = 0.00000000
0.00000000 + 38.3r + r2 = 0 + 38.54433121
38.3r + r2 = 0 + 38.54433121

Combine like terms: 0 + 38.54433121 = 38.54433121
38.3r + r2 = 38.54433121

The r term is 38.3r.  Take half its coefficient (19.15).
Square it (366.7225) and add it to both sides.

Add '366.7225' to each side of the equation.
38.3r + 366.7225 + r2 = 38.54433121 + 366.7225

Reorder the terms:
366.7225 + 38.3r + r2 = 38.54433121 + 366.7225

Combine like terms: 38.54433121 + 366.7225 = 405.26683121
366.7225 + 38.3r + r2 = 405.26683121

Factor a perfect square on the left side:
(r + 19.15)(r + 19.15) = 405.26683121

Calculate the square root of the right side: 20.131240181

Break this problem into two subproblems by setting 
(r + 19.15) equal to 20.131240181 and -20.131240181.

Subproblem 1
r + 19.15 = 20.131240181

Simplifying
r + 19.15 = 20.131240181

Reorder the terms:
19.15 + r = 20.131240181

Solving
19.15 + r = 20.131240181

Solving for variable 'r'.

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

Add '-19.15' to each side of the equation.
19.15 + -19.15 + r = 20.131240181 + -19.15

Combine like terms: 19.15 + -19.15 = 0.00
0.00 + r = 20.131240181 + -19.15
r = 20.131240181 + -19.15

Combine like terms: 20.131240181 + -19.15 = 0.981240181
r = 0.981240181

Simplifying
r = 0.981240181

Subproblem 2
r + 19.15 = -20.131240181

Simplifying
r + 19.15 = -20.131240181

Reorder the terms:
19.15 + r = -20.131240181

Solving
19.15 + r = -20.131240181

Solving for variable 'r'.

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

Add '-19.15' to each side of the equation.
19.15 + -19.15 + r = -20.131240181 + -19.15

Combine like terms: 19.15 + -19.15 = 0.00
0.00 + r = -20.131240181 + -19.15
r = -20.131240181 + -19.15

Combine like terms: -20.131240181 + -19.15 = -39.281240181
r = -39.281240181

Simplifying
r = -39.281240181

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.981240181, -39.281240181}