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Simplifying 3040 = 2 * 3.14r2 + 2 * 3.14r * 93.9 Multiply 2 * 3.14 3040 = 6.28r2 + 2 * 3.14r * 93.9 Reorder the terms for easier multiplication: 3040 = 6.28r2 + 2 * 3.14 * 93.9r Multiply 2 * 3.14 3040 = 6.28r2 + 6.28 * 93.9r Multiply 6.28 * 93.9 3040 = 6.28r2 + 589.692r Reorder the terms: 3040 = 589.692r + 6.28r2 Solving 3040 = 589.692r + 6.28r2 Solving for variable 'r'. Reorder the terms: 3040 + -589.692r + -6.28r2 = 589.692r + -589.692r + 6.28r2 + -6.28r2 Combine like terms: 589.692r + -589.692r = 0.000 3040 + -589.692r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2 3040 + -589.692r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 3040 + -589.692r + -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'. -484.0764331 + 93.9r + r2 = 0 Move the constant term to the right: Add '484.0764331' to each side of the equation. -484.0764331 + 93.9r + 484.0764331 + r2 = 0 + 484.0764331 Reorder the terms: -484.0764331 + 484.0764331 + 93.9r + r2 = 0 + 484.0764331 Combine like terms: -484.0764331 + 484.0764331 = 0.0000000 0.0000000 + 93.9r + r2 = 0 + 484.0764331 93.9r + r2 = 0 + 484.0764331 Combine like terms: 0 + 484.0764331 = 484.0764331 93.9r + r2 = 484.0764331 The r term is 93.9r. Take half its coefficient (46.95). Square it (2204.3025) and add it to both sides. Add '2204.3025' to each side of the equation. 93.9r + 2204.3025 + r2 = 484.0764331 + 2204.3025 Reorder the terms: 2204.3025 + 93.9r + r2 = 484.0764331 + 2204.3025 Combine like terms: 484.0764331 + 2204.3025 = 2688.3789331 2204.3025 + 93.9r + r2 = 2688.3789331 Factor a perfect square on the left side: (r + 46.95)(r + 46.95) = 2688.3789331 Calculate the square root of the right side: 51.849579874 Break this problem into two subproblems by setting (r + 46.95) equal to 51.849579874 and -51.849579874.Subproblem 1
r + 46.95 = 51.849579874 Simplifying r + 46.95 = 51.849579874 Reorder the terms: 46.95 + r = 51.849579874 Solving 46.95 + r = 51.849579874 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-46.95' to each side of the equation. 46.95 + -46.95 + r = 51.849579874 + -46.95 Combine like terms: 46.95 + -46.95 = 0.00 0.00 + r = 51.849579874 + -46.95 r = 51.849579874 + -46.95 Combine like terms: 51.849579874 + -46.95 = 4.899579874 r = 4.899579874 Simplifying r = 4.899579874Subproblem 2
r + 46.95 = -51.849579874 Simplifying r + 46.95 = -51.849579874 Reorder the terms: 46.95 + r = -51.849579874 Solving 46.95 + r = -51.849579874 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-46.95' to each side of the equation. 46.95 + -46.95 + r = -51.849579874 + -46.95 Combine like terms: 46.95 + -46.95 = 0.00 0.00 + r = -51.849579874 + -46.95 r = -51.849579874 + -46.95 Combine like terms: -51.849579874 + -46.95 = -98.799579874 r = -98.799579874 Simplifying r = -98.799579874Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.899579874, -98.799579874}
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