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Simplifying 742.61 = 2 * 3.14r(r) + 2 * 3.14r * 16 Multiply 2 * 3.14 742.61 = 6.28r * r + 2 * 3.14r * 16 Multiply r * r 742.61 = 6.28r2 + 2 * 3.14r * 16 Reorder the terms for easier multiplication: 742.61 = 6.28r2 + 2 * 3.14 * 16r Multiply 2 * 3.14 742.61 = 6.28r2 + 6.28 * 16r Multiply 6.28 * 16 742.61 = 6.28r2 + 100.48r Reorder the terms: 742.61 = 100.48r + 6.28r2 Solving 742.61 = 100.48r + 6.28r2 Solving for variable 'r'. Reorder the terms: 742.61 + -100.48r + -6.28r2 = 100.48r + -100.48r + 6.28r2 + -6.28r2 Combine like terms: 100.48r + -100.48r = 0.00 742.61 + -100.48r + -6.28r2 = 0.00 + 6.28r2 + -6.28r2 742.61 + -100.48r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 742.61 + -100.48r + -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'. -118.25 + 16r + r2 = 0 Move the constant term to the right: Add '118.25' to each side of the equation. -118.25 + 16r + 118.25 + r2 = 0 + 118.25 Reorder the terms: -118.25 + 118.25 + 16r + r2 = 0 + 118.25 Combine like terms: -118.25 + 118.25 = 0.00 0.00 + 16r + r2 = 0 + 118.25 16r + r2 = 0 + 118.25 Combine like terms: 0 + 118.25 = 118.25 16r + r2 = 118.25 The r term is 16r. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16r + 64 + r2 = 118.25 + 64 Reorder the terms: 64 + 16r + r2 = 118.25 + 64 Combine like terms: 118.25 + 64 = 182.25 64 + 16r + r2 = 182.25 Factor a perfect square on the left side: (r + 8)(r + 8) = 182.25 Calculate the square root of the right side: 13.5 Break this problem into two subproblems by setting (r + 8) equal to 13.5 and -13.5.Subproblem 1
r + 8 = 13.5 Simplifying r + 8 = 13.5 Reorder the terms: 8 + r = 13.5 Solving 8 + r = 13.5 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + r = 13.5 + -8 Combine like terms: 8 + -8 = 0 0 + r = 13.5 + -8 r = 13.5 + -8 Combine like terms: 13.5 + -8 = 5.5 r = 5.5 Simplifying r = 5.5Subproblem 2
r + 8 = -13.5 Simplifying r + 8 = -13.5 Reorder the terms: 8 + r = -13.5 Solving 8 + r = -13.5 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + r = -13.5 + -8 Combine like terms: 8 + -8 = 0 0 + r = -13.5 + -8 r = -13.5 + -8 Combine like terms: -13.5 + -8 = -21.5 r = -21.5 Simplifying r = -21.5Solution
The solution to the problem is based on the solutions from the subproblems. r = {5.5, -21.5}
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