3.14r^2-2(3.14)r=24(3.14)

Solution for 3.14r^2-2(3.14)r=24(3.14) equation:

Simplifying
3.14r2 + -2(3.14) * r = 24(3.14)

Multiply -2 * 3.14
3.14r2 + -6.28r = 24(3.14)

Reorder the terms:
-6.28r + 3.14r2 = 24(3.14)

Multiply 24 * 3.14
-6.28r + 3.14r2 = 75.36

Solving
-6.28r + 3.14r2 = 75.36

Solving for variable 'r'.

Reorder the terms:
-75.36 + -6.28r + 3.14r2 = 75.36 + -75.36

Combine like terms: 75.36 + -75.36 = 0.00
-75.36 + -6.28r + 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'.
-24 + -2r + r2 = 0

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + -2r + 24 + r2 = 0 + 24

Reorder the terms:
-24 + 24 + -2r + r2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -2r + r2 = 0 + 24
-2r + r2 = 0 + 24

Combine like terms: 0 + 24 = 24
-2r + r2 = 24

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 = 24 + 1

Reorder the terms:
1 + -2r + r2 = 24 + 1

Combine like terms: 24 + 1 = 25
1 + -2r + r2 = 25

Factor a perfect square on the left side:
(r + -1)(r + -1) = 25

Calculate the square root of the right side: 5

Break this problem into two subproblems by setting 
(r + -1) equal to 5 and -5.

Subproblem 1
r + -1 = 5

Simplifying
r + -1 = 5

Reorder the terms:
-1 + r = 5

Solving
-1 + r = 5

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 = 5 + 1

Combine like terms: -1 + 1 = 0
0 + r = 5 + 1
r = 5 + 1

Combine like terms: 5 + 1 = 6
r = 6

Simplifying
r = 6

Subproblem 2
r + -1 = -5

Simplifying
r + -1 = -5

Reorder the terms:
-1 + r = -5

Solving
-1 + r = -5

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 = -5 + 1

Combine like terms: -1 + 1 = 0
0 + r = -5 + 1
r = -5 + 1

Combine like terms: -5 + 1 = -4
r = -4

Simplifying
r = -4

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {6, -4}