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Simplifying 81650.99 = 2 * 3.14r2 + 2 * 3.14r * 287.8 Multiply 2 * 3.14 81650.99 = 6.28r2 + 2 * 3.14r * 287.8 Reorder the terms for easier multiplication: 81650.99 = 6.28r2 + 2 * 3.14 * 287.8r Multiply 2 * 3.14 81650.99 = 6.28r2 + 6.28 * 287.8r Multiply 6.28 * 287.8 81650.99 = 6.28r2 + 1807.384r Reorder the terms: 81650.99 = 1807.384r + 6.28r2 Solving 81650.99 = 1807.384r + 6.28r2 Solving for variable 'r'. Reorder the terms: 81650.99 + -1807.384r + -6.28r2 = 1807.384r + -1807.384r + 6.28r2 + -6.28r2 Combine like terms: 1807.384r + -1807.384r = 0.000 81650.99 + -1807.384r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2 81650.99 + -1807.384r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 81650.99 + -1807.384r + -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'. -13001.75 + 287.8r + r2 = 0 Move the constant term to the right: Add '13001.75' to each side of the equation. -13001.75 + 287.8r + 13001.75 + r2 = 0 + 13001.75 Reorder the terms: -13001.75 + 13001.75 + 287.8r + r2 = 0 + 13001.75 Combine like terms: -13001.75 + 13001.75 = 0.00 0.00 + 287.8r + r2 = 0 + 13001.75 287.8r + r2 = 0 + 13001.75 Combine like terms: 0 + 13001.75 = 13001.75 287.8r + r2 = 13001.75 The r term is 287.8r. Take half its coefficient (143.9). Square it (20707.21) and add it to both sides. Add '20707.21' to each side of the equation. 287.8r + 20707.21 + r2 = 13001.75 + 20707.21 Reorder the terms: 20707.21 + 287.8r + r2 = 13001.75 + 20707.21 Combine like terms: 13001.75 + 20707.21 = 33708.96 20707.21 + 287.8r + r2 = 33708.96 Factor a perfect square on the left side: (r + 143.9)(r + 143.9) = 33708.96 Calculate the square root of the right side: 183.6 Break this problem into two subproblems by setting (r + 143.9) equal to 183.6 and -183.6.Subproblem 1
r + 143.9 = 183.6 Simplifying r + 143.9 = 183.6 Reorder the terms: 143.9 + r = 183.6 Solving 143.9 + r = 183.6 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-143.9' to each side of the equation. 143.9 + -143.9 + r = 183.6 + -143.9 Combine like terms: 143.9 + -143.9 = 0.0 0.0 + r = 183.6 + -143.9 r = 183.6 + -143.9 Combine like terms: 183.6 + -143.9 = 39.7 r = 39.7 Simplifying r = 39.7Subproblem 2
r + 143.9 = -183.6 Simplifying r + 143.9 = -183.6 Reorder the terms: 143.9 + r = -183.6 Solving 143.9 + r = -183.6 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-143.9' to each side of the equation. 143.9 + -143.9 + r = -183.6 + -143.9 Combine like terms: 143.9 + -143.9 = 0.0 0.0 + r = -183.6 + -143.9 r = -183.6 + -143.9 Combine like terms: -183.6 + -143.9 = -327.5 r = -327.5 Simplifying r = -327.5Solution
The solution to the problem is based on the solutions from the subproblems. r = {39.7, -327.5}
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