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Simplifying 0 = 6.28r2 + 1436.864r + -44798.2544 Reorder the terms: 0 = -44798.2544 + 1436.864r + 6.28r2 Solving 0 = -44798.2544 + 1436.864r + 6.28r2 Solving for variable 'r'. Combine like terms: 0 + 44798.2544 = 44798.2544 44798.2544 + -1436.864r + -6.28r2 = -44798.2544 + 1436.864r + 6.28r2 + 44798.2544 + -1436.864r + -6.28r2 Reorder the terms: 44798.2544 + -1436.864r + -6.28r2 = -44798.2544 + 44798.2544 + 1436.864r + -1436.864r + 6.28r2 + -6.28r2 Combine like terms: -44798.2544 + 44798.2544 = 0.0000 44798.2544 + -1436.864r + -6.28r2 = 0.0000 + 1436.864r + -1436.864r + 6.28r2 + -6.28r2 44798.2544 + -1436.864r + -6.28r2 = 1436.864r + -1436.864r + 6.28r2 + -6.28r2 Combine like terms: 1436.864r + -1436.864r = 0.000 44798.2544 + -1436.864r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2 44798.2544 + -1436.864r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 44798.2544 + -1436.864r + -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'. -7133.48 + 228.8r + r2 = 0 Move the constant term to the right: Add '7133.48' to each side of the equation. -7133.48 + 228.8r + 7133.48 + r2 = 0 + 7133.48 Reorder the terms: -7133.48 + 7133.48 + 228.8r + r2 = 0 + 7133.48 Combine like terms: -7133.48 + 7133.48 = 0.00 0.00 + 228.8r + r2 = 0 + 7133.48 228.8r + r2 = 0 + 7133.48 Combine like terms: 0 + 7133.48 = 7133.48 228.8r + r2 = 7133.48 The r term is 228.8r. Take half its coefficient (114.4). Square it (13087.36) and add it to both sides. Add '13087.36' to each side of the equation. 228.8r + 13087.36 + r2 = 7133.48 + 13087.36 Reorder the terms: 13087.36 + 228.8r + r2 = 7133.48 + 13087.36 Combine like terms: 7133.48 + 13087.36 = 20220.84 13087.36 + 228.8r + r2 = 20220.84 Factor a perfect square on the left side: (r + 114.4)(r + 114.4) = 20220.84 Calculate the square root of the right side: 142.2 Break this problem into two subproblems by setting (r + 114.4) equal to 142.2 and -142.2.Subproblem 1
r + 114.4 = 142.2 Simplifying r + 114.4 = 142.2 Reorder the terms: 114.4 + r = 142.2 Solving 114.4 + r = 142.2 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-114.4' to each side of the equation. 114.4 + -114.4 + r = 142.2 + -114.4 Combine like terms: 114.4 + -114.4 = 0.0 0.0 + r = 142.2 + -114.4 r = 142.2 + -114.4 Combine like terms: 142.2 + -114.4 = 27.8 r = 27.8 Simplifying r = 27.8Subproblem 2
r + 114.4 = -142.2 Simplifying r + 114.4 = -142.2 Reorder the terms: 114.4 + r = -142.2 Solving 114.4 + r = -142.2 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-114.4' to each side of the equation. 114.4 + -114.4 + r = -142.2 + -114.4 Combine like terms: 114.4 + -114.4 = 0.0 0.0 + r = -142.2 + -114.4 r = -142.2 + -114.4 Combine like terms: -142.2 + -114.4 = -256.6 r = -256.6 Simplifying r = -256.6Solution
The solution to the problem is based on the solutions from the subproblems. r = {27.8, -256.6}
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