189.028=2*r^2*3.14+6.28*r*2.7

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Solution for 189.028=2*r^2*3.14+6.28*r*2.7 equation: 


Simplifying
189.028 = 2r2 * 3.14 + 6.28r * 2.7

Reorder the terms for easier multiplication:
189.028 = 2 * 3.14r2 + 6.28r * 2.7

Multiply 2 * 3.14
189.028 = 6.28r2 + 6.28r * 2.7

Reorder the terms for easier multiplication:
189.028 = 6.28r2 + 6.28 * 2.7r

Multiply 6.28 * 2.7
189.028 = 6.28r2 + 16.956r

Reorder the terms:
189.028 = 16.956r + 6.28r2

Solving
189.028 = 16.956r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
189.028 + -16.956r + -6.28r2 = 16.956r + -16.956r + 6.28r2 + -6.28r2

Combine like terms: 16.956r + -16.956r = 0.000
189.028 + -16.956r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
189.028 + -16.956r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
189.028 + -16.956r + -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'.
-30.1 + 2.7r + r2 = 0

Move the constant term to the right:

Add '30.1' to each side of the equation.
-30.1 + 2.7r + 30.1 + r2 = 0 + 30.1

Reorder the terms:
-30.1 + 30.1 + 2.7r + r2 = 0 + 30.1

Combine like terms: -30.1 + 30.1 = 0.0
0.0 + 2.7r + r2 = 0 + 30.1
2.7r + r2 = 0 + 30.1

Combine like terms: 0 + 30.1 = 30.1
2.7r + r2 = 30.1

The r term is 2.7r.  Take half its coefficient (1.35).
Square it (1.8225) and add it to both sides.

Add '1.8225' to each side of the equation.
2.7r + 1.8225 + r2 = 30.1 + 1.8225

Reorder the terms:
1.8225 + 2.7r + r2 = 30.1 + 1.8225

Combine like terms: 30.1 + 1.8225 = 31.9225
1.8225 + 2.7r + r2 = 31.9225

Factor a perfect square on the left side:
(r + 1.35)(r + 1.35) = 31.9225

Calculate the square root of the right side: 5.65

Break this problem into two subproblems by setting 
(r + 1.35) equal to 5.65 and -5.65.


Subproblem 1
r + 1.35 = 5.65

Simplifying
r + 1.35 = 5.65

Reorder the terms:
1.35 + r = 5.65

Solving
1.35 + r = 5.65

Solving for variable 'r'.

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

Add '-1.35' to each side of the equation.
1.35 + -1.35 + r = 5.65 + -1.35

Combine like terms: 1.35 + -1.35 = 0.00
0.00 + r = 5.65 + -1.35
r = 5.65 + -1.35

Combine like terms: 5.65 + -1.35 = 4.3
r = 4.3

Simplifying
r = 4.3


Subproblem 2
r + 1.35 = -5.65

Simplifying
r + 1.35 = -5.65

Reorder the terms:
1.35 + r = -5.65

Solving
1.35 + r = -5.65

Solving for variable 'r'.

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

Add '-1.35' to each side of the equation.
1.35 + -1.35 + r = -5.65 + -1.35

Combine like terms: 1.35 + -1.35 = 0.00
0.00 + r = -5.65 + -1.35
r = -5.65 + -1.35

Combine like terms: -5.65 + -1.35 = -7
r = -7

Simplifying
r = -7


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {4.3, -7}

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