596.7126=2*3.14*r^2+2*3.14*r*17.4

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Solution for 596.7126=2*3.14*r^2+2*3.14*r*17.4 equation: 


Simplifying
596.7126 = 2 * 3.14r2 + 2 * 3.14r * 17.4

Multiply 2 * 3.14
596.7126 = 6.28r2 + 2 * 3.14r * 17.4

Reorder the terms for easier multiplication:
596.7126 = 6.28r2 + 2 * 3.14 * 17.4r

Multiply 2 * 3.14
596.7126 = 6.28r2 + 6.28 * 17.4r

Multiply 6.28 * 17.4
596.7126 = 6.28r2 + 109.272r

Reorder the terms:
596.7126 = 109.272r + 6.28r2

Solving
596.7126 = 109.272r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
596.7126 + -109.272r + -6.28r2 = 109.272r + -109.272r + 6.28r2 + -6.28r2

Combine like terms: 109.272r + -109.272r = 0.000
596.7126 + -109.272r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
596.7126 + -109.272r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
596.7126 + -109.272r + -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'.
-95.01792994 + 17.4r + r2 = 0

Move the constant term to the right:

Add '95.01792994' to each side of the equation.
-95.01792994 + 17.4r + 95.01792994 + r2 = 0 + 95.01792994

Reorder the terms:
-95.01792994 + 95.01792994 + 17.4r + r2 = 0 + 95.01792994

Combine like terms: -95.01792994 + 95.01792994 = 0.00000000
0.00000000 + 17.4r + r2 = 0 + 95.01792994
17.4r + r2 = 0 + 95.01792994

Combine like terms: 0 + 95.01792994 = 95.01792994
17.4r + r2 = 95.01792994

The r term is 17.4r.  Take half its coefficient (8.7).
Square it (75.69) and add it to both sides.

Add '75.69' to each side of the equation.
17.4r + 75.69 + r2 = 95.01792994 + 75.69

Reorder the terms:
75.69 + 17.4r + r2 = 95.01792994 + 75.69

Combine like terms: 95.01792994 + 75.69 = 170.70792994
75.69 + 17.4r + r2 = 170.70792994

Factor a perfect square on the left side:
(r + 8.7)(r + 8.7) = 170.70792994

Calculate the square root of the right side: 13.06552448

Break this problem into two subproblems by setting 
(r + 8.7) equal to 13.06552448 and -13.06552448.


Subproblem 1
r + 8.7 = 13.06552448

Simplifying
r + 8.7 = 13.06552448

Reorder the terms:
8.7 + r = 13.06552448

Solving
8.7 + r = 13.06552448

Solving for variable 'r'.

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

Add '-8.7' to each side of the equation.
8.7 + -8.7 + r = 13.06552448 + -8.7

Combine like terms: 8.7 + -8.7 = 0.0
0.0 + r = 13.06552448 + -8.7
r = 13.06552448 + -8.7

Combine like terms: 13.06552448 + -8.7 = 4.36552448
r = 4.36552448

Simplifying
r = 4.36552448


Subproblem 2
r + 8.7 = -13.06552448

Simplifying
r + 8.7 = -13.06552448

Reorder the terms:
8.7 + r = -13.06552448

Solving
8.7 + r = -13.06552448

Solving for variable 'r'.

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

Add '-8.7' to each side of the equation.
8.7 + -8.7 + r = -13.06552448 + -8.7

Combine like terms: 8.7 + -8.7 = 0.0
0.0 + r = -13.06552448 + -8.7
r = -13.06552448 + -8.7

Combine like terms: -13.06552448 + -8.7 = -21.76552448
r = -21.76552448

Simplifying
r = -21.76552448


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {4.36552448, -21.76552448}

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