193.0472=2*3.14*r*7.7+2*3.14*r^2

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Solution for 193.0472=2*3.14*r*7.7+2*3.14*r^2 equation: 


Simplifying
193.0472 = 2 * 3.14r * 7.7 + 2 * 3.14r2

Reorder the terms for easier multiplication:
193.0472 = 2 * 3.14 * 7.7r + 2 * 3.14r2

Multiply 2 * 3.14
193.0472 = 6.28 * 7.7r + 2 * 3.14r2

Multiply 6.28 * 7.7
193.0472 = 48.356r + 2 * 3.14r2

Multiply 2 * 3.14
193.0472 = 48.356r + 6.28r2

Solving
193.0472 = 48.356r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
193.0472 + -48.356r + -6.28r2 = 48.356r + -48.356r + 6.28r2 + -6.28r2

Combine like terms: 48.356r + -48.356r = 0.000
193.0472 + -48.356r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
193.0472 + -48.356r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
193.0472 + -48.356r + -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'.
-30.74 + 7.7r + r2 = 0

Move the constant term to the right:

Add '30.74' to each side of the equation.
-30.74 + 7.7r + 30.74 + r2 = 0 + 30.74

Reorder the terms:
-30.74 + 30.74 + 7.7r + r2 = 0 + 30.74

Combine like terms: -30.74 + 30.74 = 0.00
0.00 + 7.7r + r2 = 0 + 30.74
7.7r + r2 = 0 + 30.74

Combine like terms: 0 + 30.74 = 30.74
7.7r + r2 = 30.74

The r term is 7.7r.  Take half its coefficient (3.85).
Square it (14.8225) and add it to both sides.

Add '14.8225' to each side of the equation.
7.7r + 14.8225 + r2 = 30.74 + 14.8225

Reorder the terms:
14.8225 + 7.7r + r2 = 30.74 + 14.8225

Combine like terms: 30.74 + 14.8225 = 45.5625
14.8225 + 7.7r + r2 = 45.5625

Factor a perfect square on the left side:
(r + 3.85)(r + 3.85) = 45.5625

Calculate the square root of the right side: 6.75

Break this problem into two subproblems by setting 
(r + 3.85) equal to 6.75 and -6.75.


Subproblem 1
r + 3.85 = 6.75

Simplifying
r + 3.85 = 6.75

Reorder the terms:
3.85 + r = 6.75

Solving
3.85 + r = 6.75

Solving for variable 'r'.

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

Add '-3.85' to each side of the equation.
3.85 + -3.85 + r = 6.75 + -3.85

Combine like terms: 3.85 + -3.85 = 0.00
0.00 + r = 6.75 + -3.85
r = 6.75 + -3.85

Combine like terms: 6.75 + -3.85 = 2.9
r = 2.9

Simplifying
r = 2.9


Subproblem 2
r + 3.85 = -6.75

Simplifying
r + 3.85 = -6.75

Reorder the terms:
3.85 + r = -6.75

Solving
3.85 + r = -6.75

Solving for variable 'r'.

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

Add '-3.85' to each side of the equation.
3.85 + -3.85 + r = -6.75 + -3.85

Combine like terms: 3.85 + -3.85 = 0.00
0.00 + r = -6.75 + -3.85
r = -6.75 + -3.85

Combine like terms: -6.75 + -3.85 = -10.6
r = -10.6

Simplifying
r = -10.6


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {2.9, -10.6}

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