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Simplifying 3318 = 2 * 3.14r2 + 2 * 3.14r * 36.5 Multiply 2 * 3.14 3318 = 6.28r2 + 2 * 3.14r * 36.5 Reorder the terms for easier multiplication: 3318 = 6.28r2 + 2 * 3.14 * 36.5r Multiply 2 * 3.14 3318 = 6.28r2 + 6.28 * 36.5r Multiply 6.28 * 36.5 3318 = 6.28r2 + 229.22r Reorder the terms: 3318 = 229.22r + 6.28r2 Solving 3318 = 229.22r + 6.28r2 Solving for variable 'r'. Reorder the terms: 3318 + -229.22r + -6.28r2 = 229.22r + -229.22r + 6.28r2 + -6.28r2 Combine like terms: 229.22r + -229.22r = 0.00 3318 + -229.22r + -6.28r2 = 0.00 + 6.28r2 + -6.28r2 3318 + -229.22r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 3318 + -229.22r + -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'. -528.343949 + 36.5r + r2 = 0 Move the constant term to the right: Add '528.343949' to each side of the equation. -528.343949 + 36.5r + 528.343949 + r2 = 0 + 528.343949 Reorder the terms: -528.343949 + 528.343949 + 36.5r + r2 = 0 + 528.343949 Combine like terms: -528.343949 + 528.343949 = 0.000000 0.000000 + 36.5r + r2 = 0 + 528.343949 36.5r + r2 = 0 + 528.343949 Combine like terms: 0 + 528.343949 = 528.343949 36.5r + r2 = 528.343949 The r term is 36.5r. Take half its coefficient (18.25). Square it (333.0625) and add it to both sides. Add '333.0625' to each side of the equation. 36.5r + 333.0625 + r2 = 528.343949 + 333.0625 Reorder the terms: 333.0625 + 36.5r + r2 = 528.343949 + 333.0625 Combine like terms: 528.343949 + 333.0625 = 861.406449 333.0625 + 36.5r + r2 = 861.406449 Factor a perfect square on the left side: (r + 18.25)(r + 18.25) = 861.406449 Calculate the square root of the right side: 29.349726558 Break this problem into two subproblems by setting (r + 18.25) equal to 29.349726558 and -29.349726558.Subproblem 1
r + 18.25 = 29.349726558 Simplifying r + 18.25 = 29.349726558 Reorder the terms: 18.25 + r = 29.349726558 Solving 18.25 + r = 29.349726558 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-18.25' to each side of the equation. 18.25 + -18.25 + r = 29.349726558 + -18.25 Combine like terms: 18.25 + -18.25 = 0.00 0.00 + r = 29.349726558 + -18.25 r = 29.349726558 + -18.25 Combine like terms: 29.349726558 + -18.25 = 11.099726558 r = 11.099726558 Simplifying r = 11.099726558Subproblem 2
r + 18.25 = -29.349726558 Simplifying r + 18.25 = -29.349726558 Reorder the terms: 18.25 + r = -29.349726558 Solving 18.25 + r = -29.349726558 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-18.25' to each side of the equation. 18.25 + -18.25 + r = -29.349726558 + -18.25 Combine like terms: 18.25 + -18.25 = 0.00 0.00 + r = -29.349726558 + -18.25 r = -29.349726558 + -18.25 Combine like terms: -29.349726558 + -18.25 = -47.599726558 r = -47.599726558 Simplifying r = -47.599726558Solution
The solution to the problem is based on the solutions from the subproblems. r = {11.099726558, -47.599726558}
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