2(3.14)r^2+2(3.14)r(10.6)=355.134

Solution for 2(3.14)r^2+2(3.14)r(10.6)=355.134 equation:

Simplifying
2(3.14) * r2 + 2(3.14) * r(10.6) = 355.134

Multiply 2 * 3.14
6.28r2 + 2(3.14) * r(10.6) = 355.134

Reorder the terms for easier multiplication:
6.28r2 + 2 * 3.14 * 10.6r = 355.134

Multiply 2 * 3.14
6.28r2 + 6.28 * 10.6r = 355.134

Multiply 6.28 * 10.6
6.28r2 + 66.568r = 355.134

Reorder the terms:
66.568r + 6.28r2 = 355.134

Solving
66.568r + 6.28r2 = 355.134

Solving for variable 'r'.

Reorder the terms:
-355.134 + 66.568r + 6.28r2 = 355.134 + -355.134

Combine like terms: 355.134 + -355.134 = 0.000
-355.134 + 66.568r + 6.28r2 = 0.000

Begin completing the square.  Divide all terms by
6.28 the coefficient of the squared term: 

Divide each side by '6.28'.
-56.55 + 10.6r + r2 = 0.0

Move the constant term to the right:

Add '56.55' to each side of the equation.
-56.55 + 10.6r + 56.55 + r2 = 0.0 + 56.55

Reorder the terms:
-56.55 + 56.55 + 10.6r + r2 = 0.0 + 56.55

Combine like terms: -56.55 + 56.55 = 0.00
0.00 + 10.6r + r2 = 0.0 + 56.55
10.6r + r2 = 0.0 + 56.55

Combine like terms: 0.0 + 56.55 = 56.55
10.6r + r2 = 56.55

The r term is 10.6r.  Take half its coefficient (5.3).
Square it (28.09) and add it to both sides.

Add '28.09' to each side of the equation.
10.6r + 28.09 + r2 = 56.55 + 28.09

Reorder the terms:
28.09 + 10.6r + r2 = 56.55 + 28.09

Combine like terms: 56.55 + 28.09 = 84.64
28.09 + 10.6r + r2 = 84.64

Factor a perfect square on the left side:
(r + 5.3)(r + 5.3) = 84.64

Calculate the square root of the right side: 9.2

Break this problem into two subproblems by setting 
(r + 5.3) equal to 9.2 and -9.2.

Subproblem 1
r + 5.3 = 9.2

Simplifying
r + 5.3 = 9.2

Reorder the terms:
5.3 + r = 9.2

Solving
5.3 + r = 9.2

Solving for variable 'r'.

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

Add '-5.3' to each side of the equation.
5.3 + -5.3 + r = 9.2 + -5.3

Combine like terms: 5.3 + -5.3 = 0.0
0.0 + r = 9.2 + -5.3
r = 9.2 + -5.3

Combine like terms: 9.2 + -5.3 = 3.9
r = 3.9

Simplifying
r = 3.9

Subproblem 2
r + 5.3 = -9.2

Simplifying
r + 5.3 = -9.2

Reorder the terms:
5.3 + r = -9.2

Solving
5.3 + r = -9.2

Solving for variable 'r'.

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

Add '-5.3' to each side of the equation.
5.3 + -5.3 + r = -9.2 + -5.3

Combine like terms: 5.3 + -5.3 = 0.0
0.0 + r = -9.2 + -5.3
r = -9.2 + -5.3

Combine like terms: -9.2 + -5.3 = -14.5
r = -14.5

Simplifying
r = -14.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {3.9, -14.5}