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Simplifying 16616.88 = 2 * 3.14r2 + 2 * 3.14r * 241.2 Multiply 2 * 3.14 16616.88 = 6.28r2 + 2 * 3.14r * 241.2 Reorder the terms for easier multiplication: 16616.88 = 6.28r2 + 2 * 3.14 * 241.2r Multiply 2 * 3.14 16616.88 = 6.28r2 + 6.28 * 241.2r Multiply 6.28 * 241.2 16616.88 = 6.28r2 + 1514.736r Reorder the terms: 16616.88 = 1514.736r + 6.28r2 Solving 16616.88 = 1514.736r + 6.28r2 Solving for variable 'r'. Reorder the terms: 16616.88 + -1514.736r + -6.28r2 = 1514.736r + -1514.736r + 6.28r2 + -6.28r2 Combine like terms: 1514.736r + -1514.736r = 0.000 16616.88 + -1514.736r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2 16616.88 + -1514.736r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 16616.88 + -1514.736r + -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'. -2646 + 241.2r + r2 = 0 Move the constant term to the right: Add '2646' to each side of the equation. -2646 + 241.2r + 2646 + r2 = 0 + 2646 Reorder the terms: -2646 + 2646 + 241.2r + r2 = 0 + 2646 Combine like terms: -2646 + 2646 = 0 0 + 241.2r + r2 = 0 + 2646 241.2r + r2 = 0 + 2646 Combine like terms: 0 + 2646 = 2646 241.2r + r2 = 2646 The r term is 241.2r. Take half its coefficient (120.6). Square it (14544.36) and add it to both sides. Add '14544.36' to each side of the equation. 241.2r + 14544.36 + r2 = 2646 + 14544.36 Reorder the terms: 14544.36 + 241.2r + r2 = 2646 + 14544.36 Combine like terms: 2646 + 14544.36 = 17190.36 14544.36 + 241.2r + r2 = 17190.36 Factor a perfect square on the left side: (r + 120.6)(r + 120.6) = 17190.36 Calculate the square root of the right side: 131.11201318 Break this problem into two subproblems by setting (r + 120.6) equal to 131.11201318 and -131.11201318.Subproblem 1
r + 120.6 = 131.11201318 Simplifying r + 120.6 = 131.11201318 Reorder the terms: 120.6 + r = 131.11201318 Solving 120.6 + r = 131.11201318 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-120.6' to each side of the equation. 120.6 + -120.6 + r = 131.11201318 + -120.6 Combine like terms: 120.6 + -120.6 = 0.0 0.0 + r = 131.11201318 + -120.6 r = 131.11201318 + -120.6 Combine like terms: 131.11201318 + -120.6 = 10.51201318 r = 10.51201318 Simplifying r = 10.51201318Subproblem 2
r + 120.6 = -131.11201318 Simplifying r + 120.6 = -131.11201318 Reorder the terms: 120.6 + r = -131.11201318 Solving 120.6 + r = -131.11201318 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-120.6' to each side of the equation. 120.6 + -120.6 + r = -131.11201318 + -120.6 Combine like terms: 120.6 + -120.6 = 0.0 0.0 + r = -131.11201318 + -120.6 r = -131.11201318 + -120.6 Combine like terms: -131.11201318 + -120.6 = -251.71201318 r = -251.71201318 Simplifying r = -251.71201318Solution
The solution to the problem is based on the solutions from the subproblems. r = {10.51201318, -251.71201318}
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