r^2(3.14)+2r(2)=56.52

Solution for r^2(3.14)+2r(2)=56.52 equation:

Simplifying
r2(3.14) + 2r(2) = 56.52

Reorder the terms for easier multiplication:
3.14r2 + 2r(2) = 56.52

Reorder the terms for easier multiplication:
3.14r2 + 2 * 2r = 56.52

Multiply 2 * 2
3.14r2 + 4r = 56.52

Reorder the terms:
4r + 3.14r2 = 56.52

Solving
4r + 3.14r2 = 56.52

Solving for variable 'r'.

Reorder the terms:
-56.52 + 4r + 3.14r2 = 56.52 + -56.52

Combine like terms: 56.52 + -56.52 = 0.00
-56.52 + 4r + 3.14r2 = 0.00

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

Divide each side by '3.14'.
-18 + 1.27388535r + r2 = 0

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 1.27388535r + 18 + r2 = 0 + 18

Reorder the terms:
-18 + 18 + 1.27388535r + r2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 1.27388535r + r2 = 0 + 18
1.27388535r + r2 = 0 + 18

Combine like terms: 0 + 18 = 18
1.27388535r + r2 = 18

The r term is 1.27388535r.  Take half its coefficient (0.636942675).
Square it (0.4056959712) and add it to both sides.

Add '0.4056959712' to each side of the equation.
1.27388535r + 0.4056959712 + r2 = 18 + 0.4056959712

Reorder the terms:
0.4056959712 + 1.27388535r + r2 = 18 + 0.4056959712

Combine like terms: 18 + 0.4056959712 = 18.4056959712
0.4056959712 + 1.27388535r + r2 = 18.4056959712

Factor a perfect square on the left side:
(r + 0.636942675)(r + 0.636942675) = 18.4056959712

Calculate the square root of the right side: 4.290186007

Break this problem into two subproblems by setting 
(r + 0.636942675) equal to 4.290186007 and -4.290186007.

Subproblem 1
r + 0.636942675 = 4.290186007

Simplifying
r + 0.636942675 = 4.290186007

Reorder the terms:
0.636942675 + r = 4.290186007

Solving
0.636942675 + r = 4.290186007

Solving for variable 'r'.

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

Add '-0.636942675' to each side of the equation.
0.636942675 + -0.636942675 + r = 4.290186007 + -0.636942675

Combine like terms: 0.636942675 + -0.636942675 = 0.000000000
0.000000000 + r = 4.290186007 + -0.636942675
r = 4.290186007 + -0.636942675

Combine like terms: 4.290186007 + -0.636942675 = 3.653243332
r = 3.653243332

Simplifying
r = 3.653243332

Subproblem 2
r + 0.636942675 = -4.290186007

Simplifying
r + 0.636942675 = -4.290186007

Reorder the terms:
0.636942675 + r = -4.290186007

Solving
0.636942675 + r = -4.290186007

Solving for variable 'r'.

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

Add '-0.636942675' to each side of the equation.
0.636942675 + -0.636942675 + r = -4.290186007 + -0.636942675

Combine like terms: 0.636942675 + -0.636942675 = 0.000000000
0.000000000 + r = -4.290186007 + -0.636942675
r = -4.290186007 + -0.636942675

Combine like terms: -4.290186007 + -0.636942675 = -4.927128682
r = -4.927128682

Simplifying
r = -4.927128682

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {3.653243332, -4.927128682}