141.5512=2*3.14*r*7.5+2*3.14*r^2

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Solution for 141.5512=2*3.14*r*7.5+2*3.14*r^2 equation: 


Simplifying
141.5512 = 2 * 3.14r * 7.5 + 2 * 3.14r2

Reorder the terms for easier multiplication:
141.5512 = 2 * 3.14 * 7.5r + 2 * 3.14r2

Multiply 2 * 3.14
141.5512 = 6.28 * 7.5r + 2 * 3.14r2

Multiply 6.28 * 7.5
141.5512 = 47.1r + 2 * 3.14r2

Multiply 2 * 3.14
141.5512 = 47.1r + 6.28r2

Solving
141.5512 = 47.1r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
141.5512 + -47.1r + -6.28r2 = 47.1r + -47.1r + 6.28r2 + -6.28r2

Combine like terms: 47.1r + -47.1r = 0.0
141.5512 + -47.1r + -6.28r2 = 0.0 + 6.28r2 + -6.28r2
141.5512 + -47.1r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
141.5512 + -47.1r + -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'.
-22.54 + 7.5r + r2 = 0

Move the constant term to the right:

Add '22.54' to each side of the equation.
-22.54 + 7.5r + 22.54 + r2 = 0 + 22.54

Reorder the terms:
-22.54 + 22.54 + 7.5r + r2 = 0 + 22.54

Combine like terms: -22.54 + 22.54 = 0.00
0.00 + 7.5r + r2 = 0 + 22.54
7.5r + r2 = 0 + 22.54

Combine like terms: 0 + 22.54 = 22.54
7.5r + r2 = 22.54

The r term is 7.5r.  Take half its coefficient (3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
7.5r + 14.0625 + r2 = 22.54 + 14.0625

Reorder the terms:
14.0625 + 7.5r + r2 = 22.54 + 14.0625

Combine like terms: 22.54 + 14.0625 = 36.6025
14.0625 + 7.5r + r2 = 36.6025

Factor a perfect square on the left side:
(r + 3.75)(r + 3.75) = 36.6025

Calculate the square root of the right side: 6.05

Break this problem into two subproblems by setting 
(r + 3.75) equal to 6.05 and -6.05.


Subproblem 1
r + 3.75 = 6.05

Simplifying
r + 3.75 = 6.05

Reorder the terms:
3.75 + r = 6.05

Solving
3.75 + r = 6.05

Solving for variable 'r'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + r = 6.05 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + r = 6.05 + -3.75
r = 6.05 + -3.75

Combine like terms: 6.05 + -3.75 = 2.3
r = 2.3

Simplifying
r = 2.3


Subproblem 2
r + 3.75 = -6.05

Simplifying
r + 3.75 = -6.05

Reorder the terms:
3.75 + r = -6.05

Solving
3.75 + r = -6.05

Solving for variable 'r'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + r = -6.05 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + r = -6.05 + -3.75
r = -6.05 + -3.75

Combine like terms: -6.05 + -3.75 = -9.8
r = -9.8

Simplifying
r = -9.8


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {2.3, -9.8}

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