4148.9448=2*3.14*r^2+2*3.14*r*42.5

Solution for 4148.9448=2*3.14*r^2+2*3.14*r*42.5 equation:

Simplifying
4148.9448 = 2 * 3.14r2 + 2 * 3.14r * 42.5

Multiply 2 * 3.14
4148.9448 = 6.28r2 + 2 * 3.14r * 42.5

Reorder the terms for easier multiplication:
4148.9448 = 6.28r2 + 2 * 3.14 * 42.5r

Multiply 2 * 3.14
4148.9448 = 6.28r2 + 6.28 * 42.5r

Multiply 6.28 * 42.5
4148.9448 = 6.28r2 + 266.9r

Reorder the terms:
4148.9448 = 266.9r + 6.28r2

Solving
4148.9448 = 266.9r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
4148.9448 + -266.9r + -6.28r2 = 266.9r + -266.9r + 6.28r2 + -6.28r2

Combine like terms: 266.9r + -266.9r = 0.0
4148.9448 + -266.9r + -6.28r2 = 0.0 + 6.28r2 + -6.28r2
4148.9448 + -266.9r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
4148.9448 + -266.9r + -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'.
-660.66 + 42.5r + r2 = 0

Move the constant term to the right:

Add '660.66' to each side of the equation.
-660.66 + 42.5r + 660.66 + r2 = 0 + 660.66

Reorder the terms:
-660.66 + 660.66 + 42.5r + r2 = 0 + 660.66

Combine like terms: -660.66 + 660.66 = 0.00
0.00 + 42.5r + r2 = 0 + 660.66
42.5r + r2 = 0 + 660.66

Combine like terms: 0 + 660.66 = 660.66
42.5r + r2 = 660.66

The r term is 42.5r.  Take half its coefficient (21.25).
Square it (451.5625) and add it to both sides.

Add '451.5625' to each side of the equation.
42.5r + 451.5625 + r2 = 660.66 + 451.5625

Reorder the terms:
451.5625 + 42.5r + r2 = 660.66 + 451.5625

Combine like terms: 660.66 + 451.5625 = 1112.2225
451.5625 + 42.5r + r2 = 1112.2225

Factor a perfect square on the left side:
(r + 21.25)(r + 21.25) = 1112.2225

Calculate the square root of the right side: 33.35

Break this problem into two subproblems by setting 
(r + 21.25) equal to 33.35 and -33.35.

Subproblem 1
r + 21.25 = 33.35

Simplifying
r + 21.25 = 33.35

Reorder the terms:
21.25 + r = 33.35

Solving
21.25 + r = 33.35

Solving for variable 'r'.

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

Add '-21.25' to each side of the equation.
21.25 + -21.25 + r = 33.35 + -21.25

Combine like terms: 21.25 + -21.25 = 0.00
0.00 + r = 33.35 + -21.25
r = 33.35 + -21.25

Combine like terms: 33.35 + -21.25 = 12.1
r = 12.1

Simplifying
r = 12.1

Subproblem 2
r + 21.25 = -33.35

Simplifying
r + 21.25 = -33.35

Reorder the terms:
21.25 + r = -33.35

Solving
21.25 + r = -33.35

Solving for variable 'r'.

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

Add '-21.25' to each side of the equation.
21.25 + -21.25 + r = -33.35 + -21.25

Combine like terms: 21.25 + -21.25 = 0.00
0.00 + r = -33.35 + -21.25
r = -33.35 + -21.25

Combine like terms: -33.35 + -21.25 = -54.6
r = -54.6

Simplifying
r = -54.6

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {12.1, -54.6}