3.14(r^2-2r-3)=0

Solution for 3.14(r^2-2r-3)=0 equation:

Simplifying
3.14(r2 + -2r + -3) = 0

Reorder the terms:
3.14(-3 + -2r + r2) = 0
(-3 * 3.14 + -2r * 3.14 + r2 * 3.14) = 0
(-9.42 + -6.28r + 3.14r2) = 0

Solving
-9.42 + -6.28r + 3.14r2 = 0

Solving for variable 'r'.

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

Divide each side by '3.14'.
-3 + -2r + r2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -2r + 3 + r2 = 0 + 3

Reorder the terms:
-3 + 3 + -2r + r2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2r + r2 = 0 + 3
-2r + r2 = 0 + 3

Combine like terms: 0 + 3 = 3
-2r + r2 = 3

The r term is -2r.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2r + 1 + r2 = 3 + 1

Reorder the terms:
1 + -2r + r2 = 3 + 1

Combine like terms: 3 + 1 = 4
1 + -2r + r2 = 4

Factor a perfect square on the left side:
(r + -1)(r + -1) = 4

Calculate the square root of the right side: 2

Break this problem into two subproblems by setting 
(r + -1) equal to 2 and -2.

Subproblem 1
r + -1 = 2

Simplifying
r + -1 = 2

Reorder the terms:
-1 + r = 2

Solving
-1 + r = 2

Solving for variable 'r'.

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

Add '1' to each side of the equation.
-1 + 1 + r = 2 + 1

Combine like terms: -1 + 1 = 0
0 + r = 2 + 1
r = 2 + 1

Combine like terms: 2 + 1 = 3
r = 3

Simplifying
r = 3

Subproblem 2
r + -1 = -2

Simplifying
r + -1 = -2

Reorder the terms:
-1 + r = -2

Solving
-1 + r = -2

Solving for variable 'r'.

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

Add '1' to each side of the equation.
-1 + 1 + r = -2 + 1

Combine like terms: -1 + 1 = 0
0 + r = -2 + 1
r = -2 + 1

Combine like terms: -2 + 1 = -1
r = -1

Simplifying
r = -1

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {3, -1}