2(3.14)(r^2)+2(3.14)(r)(105)=16616.88

Solution for 2(3.14)(r^2)+2(3.14)(r)(105)=16616.88 equation:

Simplifying
2(3.14)(r2) + 2(3.14)(r)(105) = 16616.88

Multiply 2 * 3.14
6.28r2 + 2(3.14)(r)(105) = 16616.88

Reorder the terms for easier multiplication:
6.28r2 + 2 * 3.14 * 105r = 16616.88

Multiply 2 * 3.14
6.28r2 + 6.28 * 105r = 16616.88

Multiply 6.28 * 105
6.28r2 + 659.4r = 16616.88

Reorder the terms:
659.4r + 6.28r2 = 16616.88

Solving
659.4r + 6.28r2 = 16616.88

Solving for variable 'r'.

Reorder the terms:
-16616.88 + 659.4r + 6.28r2 = 16616.88 + -16616.88

Combine like terms: 16616.88 + -16616.88 = 0.00
-16616.88 + 659.4r + 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'.
-2646 + 105r + r2 = 0

Move the constant term to the right:

Add '2646' to each side of the equation.
-2646 + 105r + 2646 + r2 = 0 + 2646

Reorder the terms:
-2646 + 2646 + 105r + r2 = 0 + 2646

Combine like terms: -2646 + 2646 = 0
0 + 105r + r2 = 0 + 2646
105r + r2 = 0 + 2646

Combine like terms: 0 + 2646 = 2646
105r + r2 = 2646

The r term is 105r.  Take half its coefficient (52.5).
Square it (2756.25) and add it to both sides.

Add '2756.25' to each side of the equation.
105r + 2756.25 + r2 = 2646 + 2756.25

Reorder the terms:
2756.25 + 105r + r2 = 2646 + 2756.25

Combine like terms: 2646 + 2756.25 = 5402.25
2756.25 + 105r + r2 = 5402.25

Factor a perfect square on the left side:
(r + 52.5)(r + 52.5) = 5402.25

Calculate the square root of the right side: 73.5

Break this problem into two subproblems by setting 
(r + 52.5) equal to 73.5 and -73.5.

Subproblem 1
r + 52.5 = 73.5

Simplifying
r + 52.5 = 73.5

Reorder the terms:
52.5 + r = 73.5

Solving
52.5 + r = 73.5

Solving for variable 'r'.

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

Add '-52.5' to each side of the equation.
52.5 + -52.5 + r = 73.5 + -52.5

Combine like terms: 52.5 + -52.5 = 0.0
0.0 + r = 73.5 + -52.5
r = 73.5 + -52.5

Combine like terms: 73.5 + -52.5 = 21
r = 21

Simplifying
r = 21

Subproblem 2
r + 52.5 = -73.5

Simplifying
r + 52.5 = -73.5

Reorder the terms:
52.5 + r = -73.5

Solving
52.5 + r = -73.5

Solving for variable 'r'.

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

Add '-52.5' to each side of the equation.
52.5 + -52.5 + r = -73.5 + -52.5

Combine like terms: 52.5 + -52.5 = 0.0
0.0 + r = -73.5 + -52.5
r = -73.5 + -52.5

Combine like terms: -73.5 + -52.5 = -126
r = -126

Simplifying
r = -126

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {21, -126}