569.7216=2*3.14r^2+2*3.14r*17.4

Solution for 569.7216=2*3.14r^2+2*3.14r*17.4 equation:

Simplifying
569.7216 = 2 * 3.14r2 + 2 * 3.14r * 17.4

Multiply 2 * 3.14
569.7216 = 6.28r2 + 2 * 3.14r * 17.4

Reorder the terms for easier multiplication:
569.7216 = 6.28r2 + 2 * 3.14 * 17.4r

Multiply 2 * 3.14
569.7216 = 6.28r2 + 6.28 * 17.4r

Multiply 6.28 * 17.4
569.7216 = 6.28r2 + 109.272r

Reorder the terms:
569.7216 = 109.272r + 6.28r2

Solving
569.7216 = 109.272r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
569.7216 + -109.272r + -6.28r2 = 109.272r + -109.272r + 6.28r2 + -6.28r2

Combine like terms: 109.272r + -109.272r = 0.000
569.7216 + -109.272r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
569.7216 + -109.272r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
569.7216 + -109.272r + -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'.
-90.72 + 17.4r + r2 = 0

Move the constant term to the right:

Add '90.72' to each side of the equation.
-90.72 + 17.4r + 90.72 + r2 = 0 + 90.72

Reorder the terms:
-90.72 + 90.72 + 17.4r + r2 = 0 + 90.72

Combine like terms: -90.72 + 90.72 = 0.00
0.00 + 17.4r + r2 = 0 + 90.72
17.4r + r2 = 0 + 90.72

Combine like terms: 0 + 90.72 = 90.72
17.4r + r2 = 90.72

The r term is 17.4r.  Take half its coefficient (8.7).
Square it (75.69) and add it to both sides.

Add '75.69' to each side of the equation.
17.4r + 75.69 + r2 = 90.72 + 75.69

Reorder the terms:
75.69 + 17.4r + r2 = 90.72 + 75.69

Combine like terms: 90.72 + 75.69 = 166.41
75.69 + 17.4r + r2 = 166.41

Factor a perfect square on the left side:
(r + 8.7)(r + 8.7) = 166.41

Calculate the square root of the right side: 12.9

Break this problem into two subproblems by setting 
(r + 8.7) equal to 12.9 and -12.9.

Subproblem 1
r + 8.7 = 12.9

Simplifying
r + 8.7 = 12.9

Reorder the terms:
8.7 + r = 12.9

Solving
8.7 + r = 12.9

Solving for variable 'r'.

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

Add '-8.7' to each side of the equation.
8.7 + -8.7 + r = 12.9 + -8.7

Combine like terms: 8.7 + -8.7 = 0.0
0.0 + r = 12.9 + -8.7
r = 12.9 + -8.7

Combine like terms: 12.9 + -8.7 = 4.2
r = 4.2

Simplifying
r = 4.2

Subproblem 2
r + 8.7 = -12.9

Simplifying
r + 8.7 = -12.9

Reorder the terms:
8.7 + r = -12.9

Solving
8.7 + r = -12.9

Solving for variable 'r'.

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

Add '-8.7' to each side of the equation.
8.7 + -8.7 + r = -12.9 + -8.7

Combine like terms: 8.7 + -8.7 = 0.0
0.0 + r = -12.9 + -8.7
r = -12.9 + -8.7

Combine like terms: -12.9 + -8.7 = -21.6
r = -21.6

Simplifying
r = -21.6

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {4.2, -21.6}