3234.1372=2*3.14*r^2+2*3.14*r*100.2

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Solution for 3234.1372=2*3.14*r^2+2*3.14*r*100.2 equation: 


Simplifying
3234.1372 = 2 * 3.14r2 + 2 * 3.14r * 100.2

Multiply 2 * 3.14
3234.1372 = 6.28r2 + 2 * 3.14r * 100.2

Reorder the terms for easier multiplication:
3234.1372 = 6.28r2 + 2 * 3.14 * 100.2r

Multiply 2 * 3.14
3234.1372 = 6.28r2 + 6.28 * 100.2r

Multiply 6.28 * 100.2
3234.1372 = 6.28r2 + 629.256r

Reorder the terms:
3234.1372 = 629.256r + 6.28r2

Solving
3234.1372 = 629.256r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
3234.1372 + -629.256r + -6.28r2 = 629.256r + -629.256r + 6.28r2 + -6.28r2

Combine like terms: 629.256r + -629.256r = 0.000
3234.1372 + -629.256r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
3234.1372 + -629.256r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
3234.1372 + -629.256r + -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'.
-514.99 + 100.2r + r2 = 0

Move the constant term to the right:

Add '514.99' to each side of the equation.
-514.99 + 100.2r + 514.99 + r2 = 0 + 514.99

Reorder the terms:
-514.99 + 514.99 + 100.2r + r2 = 0 + 514.99

Combine like terms: -514.99 + 514.99 = 0.00
0.00 + 100.2r + r2 = 0 + 514.99
100.2r + r2 = 0 + 514.99

Combine like terms: 0 + 514.99 = 514.99
100.2r + r2 = 514.99

The r term is 100.2r.  Take half its coefficient (50.1).
Square it (2510.01) and add it to both sides.

Add '2510.01' to each side of the equation.
100.2r + 2510.01 + r2 = 514.99 + 2510.01

Reorder the terms:
2510.01 + 100.2r + r2 = 514.99 + 2510.01

Combine like terms: 514.99 + 2510.01 = 3025
2510.01 + 100.2r + r2 = 3025

Factor a perfect square on the left side:
(r + 50.1)(r + 50.1) = 3025

Calculate the square root of the right side: 55

Break this problem into two subproblems by setting 
(r + 50.1) equal to 55 and -55.


Subproblem 1
r + 50.1 = 55

Simplifying
r + 50.1 = 55

Reorder the terms:
50.1 + r = 55

Solving
50.1 + r = 55

Solving for variable 'r'.

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

Add '-50.1' to each side of the equation.
50.1 + -50.1 + r = 55 + -50.1

Combine like terms: 50.1 + -50.1 = 0.0
0.0 + r = 55 + -50.1
r = 55 + -50.1

Combine like terms: 55 + -50.1 = 4.9
r = 4.9

Simplifying
r = 4.9


Subproblem 2
r + 50.1 = -55

Simplifying
r + 50.1 = -55

Reorder the terms:
50.1 + r = -55

Solving
50.1 + r = -55

Solving for variable 'r'.

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

Add '-50.1' to each side of the equation.
50.1 + -50.1 + r = -55 + -50.1

Combine like terms: 50.1 + -50.1 = 0.0
0.0 + r = -55 + -50.1
r = -55 + -50.1

Combine like terms: -55 + -50.1 = -105.1
r = -105.1

Simplifying
r = -105.1


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {4.9, -105.1}

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