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Simplifying 550.8816 = 6.28r2 + 101.108r Reorder the terms: 550.8816 = 101.108r + 6.28r2 Solving 550.8816 = 101.108r + 6.28r2 Solving for variable 'r'. Reorder the terms: 550.8816 + -101.108r + -6.28r2 = 101.108r + -101.108r + 6.28r2 + -6.28r2 Combine like terms: 101.108r + -101.108r = 0.000 550.8816 + -101.108r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2 550.8816 + -101.108r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 550.8816 + -101.108r + -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'. -87.72 + 16.1r + r2 = 0 Move the constant term to the right: Add '87.72' to each side of the equation. -87.72 + 16.1r + 87.72 + r2 = 0 + 87.72 Reorder the terms: -87.72 + 87.72 + 16.1r + r2 = 0 + 87.72 Combine like terms: -87.72 + 87.72 = 0.00 0.00 + 16.1r + r2 = 0 + 87.72 16.1r + r2 = 0 + 87.72 Combine like terms: 0 + 87.72 = 87.72 16.1r + r2 = 87.72 The r term is 16.1r. Take half its coefficient (8.05). Square it (64.8025) and add it to both sides. Add '64.8025' to each side of the equation. 16.1r + 64.8025 + r2 = 87.72 + 64.8025 Reorder the terms: 64.8025 + 16.1r + r2 = 87.72 + 64.8025 Combine like terms: 87.72 + 64.8025 = 152.5225 64.8025 + 16.1r + r2 = 152.5225 Factor a perfect square on the left side: (r + 8.05)(r + 8.05) = 152.5225 Calculate the square root of the right side: 12.35 Break this problem into two subproblems by setting (r + 8.05) equal to 12.35 and -12.35.Subproblem 1
r + 8.05 = 12.35 Simplifying r + 8.05 = 12.35 Reorder the terms: 8.05 + r = 12.35 Solving 8.05 + r = 12.35 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8.05' to each side of the equation. 8.05 + -8.05 + r = 12.35 + -8.05 Combine like terms: 8.05 + -8.05 = 0.00 0.00 + r = 12.35 + -8.05 r = 12.35 + -8.05 Combine like terms: 12.35 + -8.05 = 4.3 r = 4.3 Simplifying r = 4.3Subproblem 2
r + 8.05 = -12.35 Simplifying r + 8.05 = -12.35 Reorder the terms: 8.05 + r = -12.35 Solving 8.05 + r = -12.35 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8.05' to each side of the equation. 8.05 + -8.05 + r = -12.35 + -8.05 Combine like terms: 8.05 + -8.05 = 0.00 0.00 + r = -12.35 + -8.05 r = -12.35 + -8.05 Combine like terms: -12.35 + -8.05 = -20.4 r = -20.4 Simplifying r = -20.4Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.3, -20.4}
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