18079.178=2*3.14*r^2+2*3.14*r*112.4

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Solution for 18079.178=2*3.14*r^2+2*3.14*r*112.4 equation: 


Simplifying
18079.178 = 2 * 3.14r2 + 2 * 3.14r * 112.4

Multiply 2 * 3.14
18079.178 = 6.28r2 + 2 * 3.14r * 112.4

Reorder the terms for easier multiplication:
18079.178 = 6.28r2 + 2 * 3.14 * 112.4r

Multiply 2 * 3.14
18079.178 = 6.28r2 + 6.28 * 112.4r

Multiply 6.28 * 112.4
18079.178 = 6.28r2 + 705.872r

Reorder the terms:
18079.178 = 705.872r + 6.28r2

Solving
18079.178 = 705.872r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
18079.178 + -705.872r + -6.28r2 = 705.872r + -705.872r + 6.28r2 + -6.28r2

Combine like terms: 705.872r + -705.872r = 0.000
18079.178 + -705.872r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
18079.178 + -705.872r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
18079.178 + -705.872r + -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'.
-2878.85 + 112.4r + r2 = 0

Move the constant term to the right:

Add '2878.85' to each side of the equation.
-2878.85 + 112.4r + 2878.85 + r2 = 0 + 2878.85

Reorder the terms:
-2878.85 + 2878.85 + 112.4r + r2 = 0 + 2878.85

Combine like terms: -2878.85 + 2878.85 = 0.00
0.00 + 112.4r + r2 = 0 + 2878.85
112.4r + r2 = 0 + 2878.85

Combine like terms: 0 + 2878.85 = 2878.85
112.4r + r2 = 2878.85

The r term is 112.4r.  Take half its coefficient (56.2).
Square it (3158.44) and add it to both sides.

Add '3158.44' to each side of the equation.
112.4r + 3158.44 + r2 = 2878.85 + 3158.44

Reorder the terms:
3158.44 + 112.4r + r2 = 2878.85 + 3158.44

Combine like terms: 2878.85 + 3158.44 = 6037.29
3158.44 + 112.4r + r2 = 6037.29

Factor a perfect square on the left side:
(r + 56.2)(r + 56.2) = 6037.29

Calculate the square root of the right side: 77.7

Break this problem into two subproblems by setting 
(r + 56.2) equal to 77.7 and -77.7.


Subproblem 1
r + 56.2 = 77.7

Simplifying
r + 56.2 = 77.7

Reorder the terms:
56.2 + r = 77.7

Solving
56.2 + r = 77.7

Solving for variable 'r'.

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

Add '-56.2' to each side of the equation.
56.2 + -56.2 + r = 77.7 + -56.2

Combine like terms: 56.2 + -56.2 = 0.0
0.0 + r = 77.7 + -56.2
r = 77.7 + -56.2

Combine like terms: 77.7 + -56.2 = 21.5
r = 21.5

Simplifying
r = 21.5


Subproblem 2
r + 56.2 = -77.7

Simplifying
r + 56.2 = -77.7

Reorder the terms:
56.2 + r = -77.7

Solving
56.2 + r = -77.7

Solving for variable 'r'.

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

Add '-56.2' to each side of the equation.
56.2 + -56.2 + r = -77.7 + -56.2

Combine like terms: 56.2 + -56.2 = 0.0
0.0 + r = -77.7 + -56.2
r = -77.7 + -56.2

Combine like terms: -77.7 + -56.2 = -133.9
r = -133.9

Simplifying
r = -133.9


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {21.5, -133.9}

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