2(3.14)r^2+34(3.14)r=310

Solution for 2(3.14)r^2+34(3.14)r=310 equation:

Simplifying
2(3.14) * r2 + 34(3.14) * r = 310

Multiply 2 * 3.14
6.28r2 + 34(3.14) * r = 310

Multiply 34 * 3.14
6.28r2 + 106.76r = 310

Reorder the terms:
106.76r + 6.28r2 = 310

Solving
106.76r + 6.28r2 = 310

Solving for variable 'r'.

Reorder the terms:
-310 + 106.76r + 6.28r2 = 310 + -310

Combine like terms: 310 + -310 = 0
-310 + 106.76r + 6.28r2 = 0

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

Divide each side by '6.28'.
-49.36305732 + 17r + r2 = 0

Move the constant term to the right:

Add '49.36305732' to each side of the equation.
-49.36305732 + 17r + 49.36305732 + r2 = 0 + 49.36305732

Reorder the terms:
-49.36305732 + 49.36305732 + 17r + r2 = 0 + 49.36305732

Combine like terms: -49.36305732 + 49.36305732 = 0.00000000
0.00000000 + 17r + r2 = 0 + 49.36305732
17r + r2 = 0 + 49.36305732

Combine like terms: 0 + 49.36305732 = 49.36305732
17r + r2 = 49.36305732

The r term is 17r.  Take half its coefficient (8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
17r + 72.25 + r2 = 49.36305732 + 72.25

Reorder the terms:
72.25 + 17r + r2 = 49.36305732 + 72.25

Combine like terms: 49.36305732 + 72.25 = 121.61305732
72.25 + 17r + r2 = 121.61305732

Factor a perfect square on the left side:
(r + 8.5)(r + 8.5) = 121.61305732

Calculate the square root of the right side: 11.027831034

Break this problem into two subproblems by setting 
(r + 8.5) equal to 11.027831034 and -11.027831034.

Subproblem 1
r + 8.5 = 11.027831034

Simplifying
r + 8.5 = 11.027831034

Reorder the terms:
8.5 + r = 11.027831034

Solving
8.5 + r = 11.027831034

Solving for variable 'r'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + r = 11.027831034 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + r = 11.027831034 + -8.5
r = 11.027831034 + -8.5

Combine like terms: 11.027831034 + -8.5 = 2.527831034
r = 2.527831034

Simplifying
r = 2.527831034

Subproblem 2
r + 8.5 = -11.027831034

Simplifying
r + 8.5 = -11.027831034

Reorder the terms:
8.5 + r = -11.027831034

Solving
8.5 + r = -11.027831034

Solving for variable 'r'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + r = -11.027831034 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + r = -11.027831034 + -8.5
r = -11.027831034 + -8.5

Combine like terms: -11.027831034 + -8.5 = -19.527831034
r = -19.527831034

Simplifying
r = -19.527831034

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {2.527831034, -19.527831034}