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Simplifying 52611.328 = 6.28r2 + 1514.736r Reorder the terms: 52611.328 = 1514.736r + 6.28r2 Solving 52611.328 = 1514.736r + 6.28r2 Solving for variable 'r'. Reorder the terms: 52611.328 + -1514.736r + -6.28r2 = 1514.736r + -1514.736r + 6.28r2 + -6.28r2 Combine like terms: 1514.736r + -1514.736r = 0.000 52611.328 + -1514.736r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2 52611.328 + -1514.736r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 52611.328 + -1514.736r + -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'. -8377.6 + 241.2r + r2 = 0 Move the constant term to the right: Add '8377.6' to each side of the equation. -8377.6 + 241.2r + 8377.6 + r2 = 0 + 8377.6 Reorder the terms: -8377.6 + 8377.6 + 241.2r + r2 = 0 + 8377.6 Combine like terms: -8377.6 + 8377.6 = 0.0 0.0 + 241.2r + r2 = 0 + 8377.6 241.2r + r2 = 0 + 8377.6 Combine like terms: 0 + 8377.6 = 8377.6 241.2r + r2 = 8377.6 The r term is 241.2r. Take half its coefficient (120.6). Square it (14544.36) and add it to both sides. Add '14544.36' to each side of the equation. 241.2r + 14544.36 + r2 = 8377.6 + 14544.36 Reorder the terms: 14544.36 + 241.2r + r2 = 8377.6 + 14544.36 Combine like terms: 8377.6 + 14544.36 = 22921.96 14544.36 + 241.2r + r2 = 22921.96 Factor a perfect square on the left side: (r + 120.6)(r + 120.6) = 22921.96 Calculate the square root of the right side: 151.4 Break this problem into two subproblems by setting (r + 120.6) equal to 151.4 and -151.4.Subproblem 1
r + 120.6 = 151.4 Simplifying r + 120.6 = 151.4 Reorder the terms: 120.6 + r = 151.4 Solving 120.6 + r = 151.4 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-120.6' to each side of the equation. 120.6 + -120.6 + r = 151.4 + -120.6 Combine like terms: 120.6 + -120.6 = 0.0 0.0 + r = 151.4 + -120.6 r = 151.4 + -120.6 Combine like terms: 151.4 + -120.6 = 30.8 r = 30.8 Simplifying r = 30.8Subproblem 2
r + 120.6 = -151.4 Simplifying r + 120.6 = -151.4 Reorder the terms: 120.6 + r = -151.4 Solving 120.6 + r = -151.4 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-120.6' to each side of the equation. 120.6 + -120.6 + r = -151.4 + -120.6 Combine like terms: 120.6 + -120.6 = 0.0 0.0 + r = -151.4 + -120.6 r = -151.4 + -120.6 Combine like terms: -151.4 + -120.6 = -272 r = -272 Simplifying r = -272Solution
The solution to the problem is based on the solutions from the subproblems. r = {30.8, -272}
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