5645.9084=2*3.14*r^2+3.14*r*62.2*2

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Solution for 5645.9084=2*3.14*r^2+3.14*r*62.2*2 equation: 


Simplifying
5645.9084 = 2 * 3.14r2 + 3.14r * 62.2 * 2

Multiply 2 * 3.14
5645.9084 = 6.28r2 + 3.14r * 62.2 * 2

Reorder the terms for easier multiplication:
5645.9084 = 6.28r2 + 3.14 * 62.2 * 2r

Multiply 3.14 * 62.2
5645.9084 = 6.28r2 + 195.308 * 2r

Multiply 195.308 * 2
5645.9084 = 6.28r2 + 390.616r

Reorder the terms:
5645.9084 = 390.616r + 6.28r2

Solving
5645.9084 = 390.616r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
5645.9084 + -390.616r + -6.28r2 = 390.616r + -390.616r + 6.28r2 + -6.28r2

Combine like terms: 390.616r + -390.616r = 0.000
5645.9084 + -390.616r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
5645.9084 + -390.616r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
5645.9084 + -390.616r + -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'.
-899.03 + 62.2r + r2 = 0

Move the constant term to the right:

Add '899.03' to each side of the equation.
-899.03 + 62.2r + 899.03 + r2 = 0 + 899.03

Reorder the terms:
-899.03 + 899.03 + 62.2r + r2 = 0 + 899.03

Combine like terms: -899.03 + 899.03 = 0.00
0.00 + 62.2r + r2 = 0 + 899.03
62.2r + r2 = 0 + 899.03

Combine like terms: 0 + 899.03 = 899.03
62.2r + r2 = 899.03

The r term is 62.2r.  Take half its coefficient (31.1).
Square it (967.21) and add it to both sides.

Add '967.21' to each side of the equation.
62.2r + 967.21 + r2 = 899.03 + 967.21

Reorder the terms:
967.21 + 62.2r + r2 = 899.03 + 967.21

Combine like terms: 899.03 + 967.21 = 1866.24
967.21 + 62.2r + r2 = 1866.24

Factor a perfect square on the left side:
(r + 31.1)(r + 31.1) = 1866.24

Calculate the square root of the right side: 43.2

Break this problem into two subproblems by setting 
(r + 31.1) equal to 43.2 and -43.2.


Subproblem 1
r + 31.1 = 43.2

Simplifying
r + 31.1 = 43.2

Reorder the terms:
31.1 + r = 43.2

Solving
31.1 + r = 43.2

Solving for variable 'r'.

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

Add '-31.1' to each side of the equation.
31.1 + -31.1 + r = 43.2 + -31.1

Combine like terms: 31.1 + -31.1 = 0.0
0.0 + r = 43.2 + -31.1
r = 43.2 + -31.1

Combine like terms: 43.2 + -31.1 = 12.1
r = 12.1

Simplifying
r = 12.1


Subproblem 2
r + 31.1 = -43.2

Simplifying
r + 31.1 = -43.2

Reorder the terms:
31.1 + r = -43.2

Solving
31.1 + r = -43.2

Solving for variable 'r'.

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

Add '-31.1' to each side of the equation.
31.1 + -31.1 + r = -43.2 + -31.1

Combine like terms: 31.1 + -31.1 = 0.0
0.0 + r = -43.2 + -31.1
r = -43.2 + -31.1

Combine like terms: -43.2 + -31.1 = -74.3
r = -74.3

Simplifying
r = -74.3


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {12.1, -74.3}

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