453.6672=2*3.14*r^2+2*3.14*r*13

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Solution for 453.6672=2*3.14*r^2+2*3.14*r*13 equation: 


Simplifying
453.6672 = 2 * 3.14r2 + 2 * 3.14r * 13

Multiply 2 * 3.14
453.6672 = 6.28r2 + 2 * 3.14r * 13

Reorder the terms for easier multiplication:
453.6672 = 6.28r2 + 2 * 3.14 * 13r

Multiply 2 * 3.14
453.6672 = 6.28r2 + 6.28 * 13r

Multiply 6.28 * 13
453.6672 = 6.28r2 + 81.64r

Reorder the terms:
453.6672 = 81.64r + 6.28r2

Solving
453.6672 = 81.64r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
453.6672 + -81.64r + -6.28r2 = 81.64r + -81.64r + 6.28r2 + -6.28r2

Combine like terms: 81.64r + -81.64r = 0.00
453.6672 + -81.64r + -6.28r2 = 0.00 + 6.28r2 + -6.28r2
453.6672 + -81.64r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
453.6672 + -81.64r + -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'.
-72.24 + 13r + r2 = 0

Move the constant term to the right:

Add '72.24' to each side of the equation.
-72.24 + 13r + 72.24 + r2 = 0 + 72.24

Reorder the terms:
-72.24 + 72.24 + 13r + r2 = 0 + 72.24

Combine like terms: -72.24 + 72.24 = 0.00
0.00 + 13r + r2 = 0 + 72.24
13r + r2 = 0 + 72.24

Combine like terms: 0 + 72.24 = 72.24
13r + r2 = 72.24

The r term is 13r.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13r + 42.25 + r2 = 72.24 + 42.25

Reorder the terms:
42.25 + 13r + r2 = 72.24 + 42.25

Combine like terms: 72.24 + 42.25 = 114.49
42.25 + 13r + r2 = 114.49

Factor a perfect square on the left side:
(r + 6.5)(r + 6.5) = 114.49

Calculate the square root of the right side: 10.7

Break this problem into two subproblems by setting 
(r + 6.5) equal to 10.7 and -10.7.


Subproblem 1
r + 6.5 = 10.7

Simplifying
r + 6.5 = 10.7

Reorder the terms:
6.5 + r = 10.7

Solving
6.5 + r = 10.7

Solving for variable 'r'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + r = 10.7 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + r = 10.7 + -6.5
r = 10.7 + -6.5

Combine like terms: 10.7 + -6.5 = 4.2
r = 4.2

Simplifying
r = 4.2


Subproblem 2
r + 6.5 = -10.7

Simplifying
r + 6.5 = -10.7

Reorder the terms:
6.5 + r = -10.7

Solving
6.5 + r = -10.7

Solving for variable 'r'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + r = -10.7 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + r = -10.7 + -6.5
r = -10.7 + -6.5

Combine like terms: -10.7 + -6.5 = -17.2
r = -17.2

Simplifying
r = -17.2


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {4.2, -17.2}

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