0=6.28r^2+73.476r-742.61

Solution for 0=6.28r^2+73.476r-742.61 equation:

Simplifying
0 = 6.28r2 + 73.476r + -742.61

Reorder the terms:
0 = -742.61 + 73.476r + 6.28r2

Solving
0 = -742.61 + 73.476r + 6.28r2

Solving for variable 'r'.

Combine like terms: 0 + 742.61 = 742.61
742.61 + -73.476r + -6.28r2 = -742.61 + 73.476r + 6.28r2 + 742.61 + -73.476r + -6.28r2

Reorder the terms:
742.61 + -73.476r + -6.28r2 = -742.61 + 742.61 + 73.476r + -73.476r + 6.28r2 + -6.28r2

Combine like terms: -742.61 + 742.61 = 0.00
742.61 + -73.476r + -6.28r2 = 0.00 + 73.476r + -73.476r + 6.28r2 + -6.28r2
742.61 + -73.476r + -6.28r2 = 73.476r + -73.476r + 6.28r2 + -6.28r2

Combine like terms: 73.476r + -73.476r = 0.000
742.61 + -73.476r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
742.61 + -73.476r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
742.61 + -73.476r + -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'.
-118.25 + 11.7r + r2 = 0

Move the constant term to the right:

Add '118.25' to each side of the equation.
-118.25 + 11.7r + 118.25 + r2 = 0 + 118.25

Reorder the terms:
-118.25 + 118.25 + 11.7r + r2 = 0 + 118.25

Combine like terms: -118.25 + 118.25 = 0.00
0.00 + 11.7r + r2 = 0 + 118.25
11.7r + r2 = 0 + 118.25

Combine like terms: 0 + 118.25 = 118.25
11.7r + r2 = 118.25

The r term is 11.7r.  Take half its coefficient (5.85).
Square it (34.2225) and add it to both sides.

Add '34.2225' to each side of the equation.
11.7r + 34.2225 + r2 = 118.25 + 34.2225

Reorder the terms:
34.2225 + 11.7r + r2 = 118.25 + 34.2225

Combine like terms: 118.25 + 34.2225 = 152.4725
34.2225 + 11.7r + r2 = 152.4725

Factor a perfect square on the left side:
(r + 5.85)(r + 5.85) = 152.4725

Calculate the square root of the right side: 12.347975543

Break this problem into two subproblems by setting 
(r + 5.85) equal to 12.347975543 and -12.347975543.

Subproblem 1
r + 5.85 = 12.347975543

Simplifying
r + 5.85 = 12.347975543

Reorder the terms:
5.85 + r = 12.347975543

Solving
5.85 + r = 12.347975543

Solving for variable 'r'.

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

Add '-5.85' to each side of the equation.
5.85 + -5.85 + r = 12.347975543 + -5.85

Combine like terms: 5.85 + -5.85 = 0.00
0.00 + r = 12.347975543 + -5.85
r = 12.347975543 + -5.85

Combine like terms: 12.347975543 + -5.85 = 6.497975543
r = 6.497975543

Simplifying
r = 6.497975543

Subproblem 2
r + 5.85 = -12.347975543

Simplifying
r + 5.85 = -12.347975543

Reorder the terms:
5.85 + r = -12.347975543

Solving
5.85 + r = -12.347975543

Solving for variable 'r'.

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

Add '-5.85' to each side of the equation.
5.85 + -5.85 + r = -12.347975543 + -5.85

Combine like terms: 5.85 + -5.85 = 0.00
0.00 + r = -12.347975543 + -5.85
r = -12.347975543 + -5.85

Combine like terms: -12.347975543 + -5.85 = -18.197975543
r = -18.197975543

Simplifying
r = -18.197975543

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {6.497975543, -18.197975543}