591.3876=2*3.14r^2+2*3.14r*17.6

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Solution for 591.3876=2*3.14r^2+2*3.14r*17.6 equation: 


Simplifying
591.3876 = 2 * 3.14r2 + 2 * 3.14r * 17.6

Multiply 2 * 3.14
591.3876 = 6.28r2 + 2 * 3.14r * 17.6

Reorder the terms for easier multiplication:
591.3876 = 6.28r2 + 2 * 3.14 * 17.6r

Multiply 2 * 3.14
591.3876 = 6.28r2 + 6.28 * 17.6r

Multiply 6.28 * 17.6
591.3876 = 6.28r2 + 110.528r

Reorder the terms:
591.3876 = 110.528r + 6.28r2

Solving
591.3876 = 110.528r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
591.3876 + -110.528r + -6.28r2 = 110.528r + -110.528r + 6.28r2 + -6.28r2

Combine like terms: 110.528r + -110.528r = 0.000
591.3876 + -110.528r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
591.3876 + -110.528r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
591.3876 + -110.528r + -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'.
-94.17 + 17.6r + r2 = 0

Move the constant term to the right:

Add '94.17' to each side of the equation.
-94.17 + 17.6r + 94.17 + r2 = 0 + 94.17

Reorder the terms:
-94.17 + 94.17 + 17.6r + r2 = 0 + 94.17

Combine like terms: -94.17 + 94.17 = 0.00
0.00 + 17.6r + r2 = 0 + 94.17
17.6r + r2 = 0 + 94.17

Combine like terms: 0 + 94.17 = 94.17
17.6r + r2 = 94.17

The r term is 17.6r.  Take half its coefficient (8.8).
Square it (77.44) and add it to both sides.

Add '77.44' to each side of the equation.
17.6r + 77.44 + r2 = 94.17 + 77.44

Reorder the terms:
77.44 + 17.6r + r2 = 94.17 + 77.44

Combine like terms: 94.17 + 77.44 = 171.61
77.44 + 17.6r + r2 = 171.61

Factor a perfect square on the left side:
(r + 8.8)(r + 8.8) = 171.61

Calculate the square root of the right side: 13.1

Break this problem into two subproblems by setting 
(r + 8.8) equal to 13.1 and -13.1.


Subproblem 1
r + 8.8 = 13.1

Simplifying
r + 8.8 = 13.1

Reorder the terms:
8.8 + r = 13.1

Solving
8.8 + r = 13.1

Solving for variable 'r'.

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

Add '-8.8' to each side of the equation.
8.8 + -8.8 + r = 13.1 + -8.8

Combine like terms: 8.8 + -8.8 = 0.0
0.0 + r = 13.1 + -8.8
r = 13.1 + -8.8

Combine like terms: 13.1 + -8.8 = 4.3
r = 4.3

Simplifying
r = 4.3


Subproblem 2
r + 8.8 = -13.1

Simplifying
r + 8.8 = -13.1

Reorder the terms:
8.8 + r = -13.1

Solving
8.8 + r = -13.1

Solving for variable 'r'.

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

Add '-8.8' to each side of the equation.
8.8 + -8.8 + r = -13.1 + -8.8

Combine like terms: 8.8 + -8.8 = 0.0
0.0 + r = -13.1 + -8.8
r = -13.1 + -8.8

Combine like terms: -13.1 + -8.8 = -21.9
r = -21.9

Simplifying
r = -21.9


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {4.3, -21.9}

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