3602.48=2*3.14*r^2+2*3.14*r*95

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Solution for 3602.48=2*3.14*r^2+2*3.14*r*95 equation:


Simplifying
3602.48 = 2 * 3.14r2 + 2 * 3.14r * 95

Multiply 2 * 3.14
3602.48 = 6.28r2 + 2 * 3.14r * 95

Reorder the terms for easier multiplication:
3602.48 = 6.28r2 + 2 * 3.14 * 95r

Multiply 2 * 3.14
3602.48 = 6.28r2 + 6.28 * 95r

Multiply 6.28 * 95
3602.48 = 6.28r2 + 596.6r

Reorder the terms:
3602.48 = 596.6r + 6.28r2

Solving
3602.48 = 596.6r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
3602.48 + -596.6r + -6.28r2 = 596.6r + -596.6r + 6.28r2 + -6.28r2

Combine like terms: 596.6r + -596.6r = 0.0
3602.48 + -596.6r + -6.28r2 = 0.0 + 6.28r2 + -6.28r2
3602.48 + -596.6r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
3602.48 + -596.6r + -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'.
-573.6433121 + 95r + r2 = 0

Move the constant term to the right:

Add '573.6433121' to each side of the equation.
-573.6433121 + 95r + 573.6433121 + r2 = 0 + 573.6433121

Reorder the terms:
-573.6433121 + 573.6433121 + 95r + r2 = 0 + 573.6433121

Combine like terms: -573.6433121 + 573.6433121 = 0.0000000
0.0000000 + 95r + r2 = 0 + 573.6433121
95r + r2 = 0 + 573.6433121

Combine like terms: 0 + 573.6433121 = 573.6433121
95r + r2 = 573.6433121

The r term is 95r.  Take half its coefficient (47.5).
Square it (2256.25) and add it to both sides.

Add '2256.25' to each side of the equation.
95r + 2256.25 + r2 = 573.6433121 + 2256.25

Reorder the terms:
2256.25 + 95r + r2 = 573.6433121 + 2256.25

Combine like terms: 573.6433121 + 2256.25 = 2829.8933121
2256.25 + 95r + r2 = 2829.8933121

Factor a perfect square on the left side:
(r + 47.5)(r + 47.5) = 2829.8933121

Calculate the square root of the right side: 53.196741555

Break this problem into two subproblems by setting 
(r + 47.5) equal to 53.196741555 and -53.196741555.

Subproblem 1

r + 47.5 = 53.196741555 Simplifying r + 47.5 = 53.196741555 Reorder the terms: 47.5 + r = 53.196741555 Solving 47.5 + r = 53.196741555 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-47.5' to each side of the equation. 47.5 + -47.5 + r = 53.196741555 + -47.5 Combine like terms: 47.5 + -47.5 = 0.0 0.0 + r = 53.196741555 + -47.5 r = 53.196741555 + -47.5 Combine like terms: 53.196741555 + -47.5 = 5.696741555 r = 5.696741555 Simplifying r = 5.696741555

Subproblem 2

r + 47.5 = -53.196741555 Simplifying r + 47.5 = -53.196741555 Reorder the terms: 47.5 + r = -53.196741555 Solving 47.5 + r = -53.196741555 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-47.5' to each side of the equation. 47.5 + -47.5 + r = -53.196741555 + -47.5 Combine like terms: 47.5 + -47.5 = 0.0 0.0 + r = -53.196741555 + -47.5 r = -53.196741555 + -47.5 Combine like terms: -53.196741555 + -47.5 = -100.696741555 r = -100.696741555 Simplifying r = -100.696741555

Solution

The solution to the problem is based on the solutions from the subproblems. r = {5.696741555, -100.696741555}

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