11124.393=2*3.14*r^2+2*3.14*r*82.2

Solution for 11124.393=2*3.14*r^2+2*3.14*r*82.2 equation:

Simplifying
11124.393 = 2 * 3.14r2 + 2 * 3.14r * 82.2

Multiply 2 * 3.14
11124.393 = 6.28r2 + 2 * 3.14r * 82.2

Reorder the terms for easier multiplication:
11124.393 = 6.28r2 + 2 * 3.14 * 82.2r

Multiply 2 * 3.14
11124.393 = 6.28r2 + 6.28 * 82.2r

Multiply 6.28 * 82.2
11124.393 = 6.28r2 + 516.216r

Reorder the terms:
11124.393 = 516.216r + 6.28r2

Solving
11124.393 = 516.216r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
11124.393 + -516.216r + -6.28r2 = 516.216r + -516.216r + 6.28r2 + -6.28r2

Combine like terms: 516.216r + -516.216r = 0.000
11124.393 + -516.216r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
11124.393 + -516.216r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
11124.393 + -516.216r + -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'.
-1771.400159 + 82.2r + r2 = 0

Move the constant term to the right:

Add '1771.400159' to each side of the equation.
-1771.400159 + 82.2r + 1771.400159 + r2 = 0 + 1771.400159

Reorder the terms:
-1771.400159 + 1771.400159 + 82.2r + r2 = 0 + 1771.400159

Combine like terms: -1771.400159 + 1771.400159 = 0.000000
0.000000 + 82.2r + r2 = 0 + 1771.400159
82.2r + r2 = 0 + 1771.400159

Combine like terms: 0 + 1771.400159 = 1771.400159
82.2r + r2 = 1771.400159

The r term is 82.2r.  Take half its coefficient (41.1).
Square it (1689.21) and add it to both sides.

Add '1689.21' to each side of the equation.
82.2r + 1689.21 + r2 = 1771.400159 + 1689.21

Reorder the terms:
1689.21 + 82.2r + r2 = 1771.400159 + 1689.21

Combine like terms: 1771.400159 + 1689.21 = 3460.610159
1689.21 + 82.2r + r2 = 3460.610159

Factor a perfect square on the left side:
(r + 41.1)(r + 41.1) = 3460.610159

Calculate the square root of the right side: 58.826950958

Break this problem into two subproblems by setting 
(r + 41.1) equal to 58.826950958 and -58.826950958.

Subproblem 1
r + 41.1 = 58.826950958

Simplifying
r + 41.1 = 58.826950958

Reorder the terms:
41.1 + r = 58.826950958

Solving
41.1 + r = 58.826950958

Solving for variable 'r'.

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

Add '-41.1' to each side of the equation.
41.1 + -41.1 + r = 58.826950958 + -41.1

Combine like terms: 41.1 + -41.1 = 0.0
0.0 + r = 58.826950958 + -41.1
r = 58.826950958 + -41.1

Combine like terms: 58.826950958 + -41.1 = 17.726950958
r = 17.726950958

Simplifying
r = 17.726950958

Subproblem 2
r + 41.1 = -58.826950958

Simplifying
r + 41.1 = -58.826950958

Reorder the terms:
41.1 + r = -58.826950958

Solving
41.1 + r = -58.826950958

Solving for variable 'r'.

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

Add '-41.1' to each side of the equation.
41.1 + -41.1 + r = -58.826950958 + -41.1

Combine like terms: 41.1 + -41.1 = 0.0
0.0 + r = -58.826950958 + -41.1
r = -58.826950958 + -41.1

Combine like terms: -58.826950958 + -41.1 = -99.926950958
r = -99.926950958

Simplifying
r = -99.926950958

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {17.726950958, -99.926950958}