648(3.14)=2(3.14)r(15)+2r^2

Solution for 648(3.14)=2(3.14)r(15)+2r^2 equation:

Simplifying
648(3.14) = 2(3.14) * r(15) + 2r2

Multiply 648 * 3.14
2034.72 = 2(3.14) * r(15) + 2r2

Reorder the terms for easier multiplication:
2034.72 = 2 * 3.14 * 15r + 2r2

Multiply 2 * 3.14
2034.72 = 6.28 * 15r + 2r2

Multiply 6.28 * 15
2034.72 = 94.2r + 2r2

Solving
2034.72 = 94.2r + 2r2

Solving for variable 'r'.

Reorder the terms:
2034.72 + -94.2r + -2r2 = 94.2r + -94.2r + 2r2 + -2r2

Combine like terms: 94.2r + -94.2r = 0.0
2034.72 + -94.2r + -2r2 = 0.0 + 2r2 + -2r2
2034.72 + -94.2r + -2r2 = 2r2 + -2r2

Combine like terms: 2r2 + -2r2 = 0
2034.72 + -94.2r + -2r2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-1017.36 + 47.1r + r2 = 0

Move the constant term to the right:

Add '1017.36' to each side of the equation.
-1017.36 + 47.1r + 1017.36 + r2 = 0 + 1017.36

Reorder the terms:
-1017.36 + 1017.36 + 47.1r + r2 = 0 + 1017.36

Combine like terms: -1017.36 + 1017.36 = 0.00
0.00 + 47.1r + r2 = 0 + 1017.36
47.1r + r2 = 0 + 1017.36

Combine like terms: 0 + 1017.36 = 1017.36
47.1r + r2 = 1017.36

The r term is 47.1r.  Take half its coefficient (23.55).
Square it (554.6025) and add it to both sides.

Add '554.6025' to each side of the equation.
47.1r + 554.6025 + r2 = 1017.36 + 554.6025

Reorder the terms:
554.6025 + 47.1r + r2 = 1017.36 + 554.6025

Combine like terms: 1017.36 + 554.6025 = 1571.9625
554.6025 + 47.1r + r2 = 1571.9625

Factor a perfect square on the left side:
(r + 23.55)(r + 23.55) = 1571.9625

Calculate the square root of the right side: 39.647982294

Break this problem into two subproblems by setting 
(r + 23.55) equal to 39.647982294 and -39.647982294.

Subproblem 1
r + 23.55 = 39.647982294

Simplifying
r + 23.55 = 39.647982294

Reorder the terms:
23.55 + r = 39.647982294

Solving
23.55 + r = 39.647982294

Solving for variable 'r'.

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

Add '-23.55' to each side of the equation.
23.55 + -23.55 + r = 39.647982294 + -23.55

Combine like terms: 23.55 + -23.55 = 0.00
0.00 + r = 39.647982294 + -23.55
r = 39.647982294 + -23.55

Combine like terms: 39.647982294 + -23.55 = 16.097982294
r = 16.097982294

Simplifying
r = 16.097982294

Subproblem 2
r + 23.55 = -39.647982294

Simplifying
r + 23.55 = -39.647982294

Reorder the terms:
23.55 + r = -39.647982294

Solving
23.55 + r = -39.647982294

Solving for variable 'r'.

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

Add '-23.55' to each side of the equation.
23.55 + -23.55 + r = -39.647982294 + -23.55

Combine like terms: 23.55 + -23.55 = 0.00
0.00 + r = -39.647982294 + -23.55
r = -39.647982294 + -23.55

Combine like terms: -39.647982294 + -23.55 = -63.197982294
r = -63.197982294

Simplifying
r = -63.197982294

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {16.097982294, -63.197982294}