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Simplifying 13602.48 = 2 * 3.14r2 + 2 * 3.14r * 95 Multiply 2 * 3.14 13602.48 = 6.28r2 + 2 * 3.14r * 95 Reorder the terms for easier multiplication: 13602.48 = 6.28r2 + 2 * 3.14 * 95r Multiply 2 * 3.14 13602.48 = 6.28r2 + 6.28 * 95r Multiply 6.28 * 95 13602.48 = 6.28r2 + 596.6r Reorder the terms: 13602.48 = 596.6r + 6.28r2 Solving 13602.48 = 596.6r + 6.28r2 Solving for variable 'r'. Reorder the terms: 13602.48 + -596.6r + -6.28r2 = 596.6r + -596.6r + 6.28r2 + -6.28r2 Combine like terms: 596.6r + -596.6r = 0.0 13602.48 + -596.6r + -6.28r2 = 0.0 + 6.28r2 + -6.28r2 13602.48 + -596.6r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 13602.48 + -596.6r + -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'. -2166 + 95r + r2 = 0 Move the constant term to the right: Add '2166' to each side of the equation. -2166 + 95r + 2166 + r2 = 0 + 2166 Reorder the terms: -2166 + 2166 + 95r + r2 = 0 + 2166 Combine like terms: -2166 + 2166 = 0 0 + 95r + r2 = 0 + 2166 95r + r2 = 0 + 2166 Combine like terms: 0 + 2166 = 2166 95r + r2 = 2166 The r term is 95r. Take half its coefficient (47.5). Square it (2256.25) and add it to both sides. Add '2256.25' to each side of the equation. 95r + 2256.25 + r2 = 2166 + 2256.25 Reorder the terms: 2256.25 + 95r + r2 = 2166 + 2256.25 Combine like terms: 2166 + 2256.25 = 4422.25 2256.25 + 95r + r2 = 4422.25 Factor a perfect square on the left side: (r + 47.5)(r + 47.5) = 4422.25 Calculate the square root of the right side: 66.5 Break this problem into two subproblems by setting (r + 47.5) equal to 66.5 and -66.5.Subproblem 1
r + 47.5 = 66.5 Simplifying r + 47.5 = 66.5 Reorder the terms: 47.5 + r = 66.5 Solving 47.5 + r = 66.5 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-47.5' to each side of the equation. 47.5 + -47.5 + r = 66.5 + -47.5 Combine like terms: 47.5 + -47.5 = 0.0 0.0 + r = 66.5 + -47.5 r = 66.5 + -47.5 Combine like terms: 66.5 + -47.5 = 19 r = 19 Simplifying r = 19Subproblem 2
r + 47.5 = -66.5 Simplifying r + 47.5 = -66.5 Reorder the terms: 47.5 + r = -66.5 Solving 47.5 + r = -66.5 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-47.5' to each side of the equation. 47.5 + -47.5 + r = -66.5 + -47.5 Combine like terms: 47.5 + -47.5 = 0.0 0.0 + r = -66.5 + -47.5 r = -66.5 + -47.5 Combine like terms: -66.5 + -47.5 = -114 r = -114 Simplifying r = -114Solution
The solution to the problem is based on the solutions from the subproblems. r = {19, -114}
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