3.14(r^2-2r-80)=0

Solution for 3.14(r^2-2r-80)=0 equation:

Simplifying
3.14(r2 + -2r + -80) = 0

Reorder the terms:
3.14(-80 + -2r + r2) = 0
(-80 * 3.14 + -2r * 3.14 + r2 * 3.14) = 0
(-251.2 + -6.28r + 3.14r2) = 0

Solving
-251.2 + -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'.
-80 + -2r + r2 = 0

Move the constant term to the right:

Add '80' to each side of the equation.
-80 + -2r + 80 + r2 = 0 + 80

Reorder the terms:
-80 + 80 + -2r + r2 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + -2r + r2 = 0 + 80
-2r + r2 = 0 + 80

Combine like terms: 0 + 80 = 80
-2r + r2 = 80

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 = 80 + 1

Reorder the terms:
1 + -2r + r2 = 80 + 1

Combine like terms: 80 + 1 = 81
1 + -2r + r2 = 81

Factor a perfect square on the left side:
(r + -1)(r + -1) = 81

Calculate the square root of the right side: 9

Break this problem into two subproblems by setting 
(r + -1) equal to 9 and -9.

Subproblem 1
r + -1 = 9

Simplifying
r + -1 = 9

Reorder the terms:
-1 + r = 9

Solving
-1 + r = 9

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 = 9 + 1

Combine like terms: -1 + 1 = 0
0 + r = 9 + 1
r = 9 + 1

Combine like terms: 9 + 1 = 10
r = 10

Simplifying
r = 10

Subproblem 2
r + -1 = -9

Simplifying
r + -1 = -9

Reorder the terms:
-1 + r = -9

Solving
-1 + r = -9

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 = -9 + 1

Combine like terms: -1 + 1 = 0
0 + r = -9 + 1
r = -9 + 1

Combine like terms: -9 + 1 = -8
r = -8

Simplifying
r = -8

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {10, -8}