1133.9168=2*3.14*r^2+2*3.14*r*23.5

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Solution for 1133.9168=2*3.14*r^2+2*3.14*r*23.5 equation: 


Simplifying
1133.9168 = 2 * 3.14r2 + 2 * 3.14r * 23.5

Multiply 2 * 3.14
1133.9168 = 6.28r2 + 2 * 3.14r * 23.5

Reorder the terms for easier multiplication:
1133.9168 = 6.28r2 + 2 * 3.14 * 23.5r

Multiply 2 * 3.14
1133.9168 = 6.28r2 + 6.28 * 23.5r

Multiply 6.28 * 23.5
1133.9168 = 6.28r2 + 147.58r

Reorder the terms:
1133.9168 = 147.58r + 6.28r2

Solving
1133.9168 = 147.58r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
1133.9168 + -147.58r + -6.28r2 = 147.58r + -147.58r + 6.28r2 + -6.28r2

Combine like terms: 147.58r + -147.58r = 0.00
1133.9168 + -147.58r + -6.28r2 = 0.00 + 6.28r2 + -6.28r2
1133.9168 + -147.58r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
1133.9168 + -147.58r + -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'.
-180.56 + 23.5r + r2 = 0

Move the constant term to the right:

Add '180.56' to each side of the equation.
-180.56 + 23.5r + 180.56 + r2 = 0 + 180.56

Reorder the terms:
-180.56 + 180.56 + 23.5r + r2 = 0 + 180.56

Combine like terms: -180.56 + 180.56 = 0.00
0.00 + 23.5r + r2 = 0 + 180.56
23.5r + r2 = 0 + 180.56

Combine like terms: 0 + 180.56 = 180.56
23.5r + r2 = 180.56

The r term is 23.5r.  Take half its coefficient (11.75).
Square it (138.0625) and add it to both sides.

Add '138.0625' to each side of the equation.
23.5r + 138.0625 + r2 = 180.56 + 138.0625

Reorder the terms:
138.0625 + 23.5r + r2 = 180.56 + 138.0625

Combine like terms: 180.56 + 138.0625 = 318.6225
138.0625 + 23.5r + r2 = 318.6225

Factor a perfect square on the left side:
(r + 11.75)(r + 11.75) = 318.6225

Calculate the square root of the right side: 17.85

Break this problem into two subproblems by setting 
(r + 11.75) equal to 17.85 and -17.85.


Subproblem 1
r + 11.75 = 17.85

Simplifying
r + 11.75 = 17.85

Reorder the terms:
11.75 + r = 17.85

Solving
11.75 + r = 17.85

Solving for variable 'r'.

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

Add '-11.75' to each side of the equation.
11.75 + -11.75 + r = 17.85 + -11.75

Combine like terms: 11.75 + -11.75 = 0.00
0.00 + r = 17.85 + -11.75
r = 17.85 + -11.75

Combine like terms: 17.85 + -11.75 = 6.1
r = 6.1

Simplifying
r = 6.1


Subproblem 2
r + 11.75 = -17.85

Simplifying
r + 11.75 = -17.85

Reorder the terms:
11.75 + r = -17.85

Solving
11.75 + r = -17.85

Solving for variable 'r'.

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

Add '-11.75' to each side of the equation.
11.75 + -11.75 + r = -17.85 + -11.75

Combine like terms: 11.75 + -11.75 = 0.00
0.00 + r = -17.85 + -11.75
r = -17.85 + -11.75

Combine like terms: -17.85 + -11.75 = -29.6
r = -29.6

Simplifying
r = -29.6


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {6.1, -29.6}

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