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Simplifying 8034.4 = 2 * 3.14r2 + 2 * 3.14r * 64 Multiply 2 * 3.14 8034.4 = 6.28r2 + 2 * 3.14r * 64 Reorder the terms for easier multiplication: 8034.4 = 6.28r2 + 2 * 3.14 * 64r Multiply 2 * 3.14 8034.4 = 6.28r2 + 6.28 * 64r Multiply 6.28 * 64 8034.4 = 6.28r2 + 401.92r Reorder the terms: 8034.4 = 401.92r + 6.28r2 Solving 8034.4 = 401.92r + 6.28r2 Solving for variable 'r'. Reorder the terms: 8034.4 + -401.92r + -6.28r2 = 401.92r + -401.92r + 6.28r2 + -6.28r2 Combine like terms: 401.92r + -401.92r = 0.00 8034.4 + -401.92r + -6.28r2 = 0.00 + 6.28r2 + -6.28r2 8034.4 + -401.92r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 8034.4 + -401.92r + -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'. -1279.363057 + 64r + r2 = 0 Move the constant term to the right: Add '1279.363057' to each side of the equation. -1279.363057 + 64r + 1279.363057 + r2 = 0 + 1279.363057 Reorder the terms: -1279.363057 + 1279.363057 + 64r + r2 = 0 + 1279.363057 Combine like terms: -1279.363057 + 1279.363057 = 0.000000 0.000000 + 64r + r2 = 0 + 1279.363057 64r + r2 = 0 + 1279.363057 Combine like terms: 0 + 1279.363057 = 1279.363057 64r + r2 = 1279.363057 The r term is 64r. Take half its coefficient (32). Square it (1024) and add it to both sides. Add '1024' to each side of the equation. 64r + 1024 + r2 = 1279.363057 + 1024 Reorder the terms: 1024 + 64r + r2 = 1279.363057 + 1024 Combine like terms: 1279.363057 + 1024 = 2303.363057 1024 + 64r + r2 = 2303.363057 Factor a perfect square on the left side: (r + 32)(r + 32) = 2303.363057 Calculate the square root of the right side: 47.993364718 Break this problem into two subproblems by setting (r + 32) equal to 47.993364718 and -47.993364718.Subproblem 1
r + 32 = 47.993364718 Simplifying r + 32 = 47.993364718 Reorder the terms: 32 + r = 47.993364718 Solving 32 + r = 47.993364718 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + r = 47.993364718 + -32 Combine like terms: 32 + -32 = 0 0 + r = 47.993364718 + -32 r = 47.993364718 + -32 Combine like terms: 47.993364718 + -32 = 15.993364718 r = 15.993364718 Simplifying r = 15.993364718Subproblem 2
r + 32 = -47.993364718 Simplifying r + 32 = -47.993364718 Reorder the terms: 32 + r = -47.993364718 Solving 32 + r = -47.993364718 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + r = -47.993364718 + -32 Combine like terms: 32 + -32 = 0 0 + r = -47.993364718 + -32 r = -47.993364718 + -32 Combine like terms: -47.993364718 + -32 = -79.993364718 r = -79.993364718 Simplifying r = -79.993364718Solution
The solution to the problem is based on the solutions from the subproblems. r = {15.993364718, -79.993364718}
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