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Simplifying 44798.2544 = 6.28r2 + 1813.664r Reorder the terms: 44798.2544 = 1813.664r + 6.28r2 Solving 44798.2544 = 1813.664r + 6.28r2 Solving for variable 'r'. Reorder the terms: 44798.2544 + -1813.664r + -6.28r2 = 1813.664r + -1813.664r + 6.28r2 + -6.28r2 Combine like terms: 1813.664r + -1813.664r = 0.000 44798.2544 + -1813.664r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2 44798.2544 + -1813.664r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 44798.2544 + -1813.664r + -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 + 288.8r + r2 = 0 Move the constant term to the right: Add '7133.48' to each side of the equation. -7133.48 + 288.8r + 7133.48 + r2 = 0 + 7133.48 Reorder the terms: -7133.48 + 7133.48 + 288.8r + r2 = 0 + 7133.48 Combine like terms: -7133.48 + 7133.48 = 0.00 0.00 + 288.8r + r2 = 0 + 7133.48 288.8r + r2 = 0 + 7133.48 Combine like terms: 0 + 7133.48 = 7133.48 288.8r + r2 = 7133.48 The r term is 288.8r. Take half its coefficient (144.4). Square it (20851.36) and add it to both sides. Add '20851.36' to each side of the equation. 288.8r + 20851.36 + r2 = 7133.48 + 20851.36 Reorder the terms: 20851.36 + 288.8r + r2 = 7133.48 + 20851.36 Combine like terms: 7133.48 + 20851.36 = 27984.84 20851.36 + 288.8r + r2 = 27984.84 Factor a perfect square on the left side: (r + 144.4)(r + 144.4) = 27984.84 Calculate the square root of the right side: 167.286700009 Break this problem into two subproblems by setting (r + 144.4) equal to 167.286700009 and -167.286700009.Subproblem 1
r + 144.4 = 167.286700009 Simplifying r + 144.4 = 167.286700009 Reorder the terms: 144.4 + r = 167.286700009 Solving 144.4 + r = 167.286700009 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-144.4' to each side of the equation. 144.4 + -144.4 + r = 167.286700009 + -144.4 Combine like terms: 144.4 + -144.4 = 0.0 0.0 + r = 167.286700009 + -144.4 r = 167.286700009 + -144.4 Combine like terms: 167.286700009 + -144.4 = 22.886700009 r = 22.886700009 Simplifying r = 22.886700009Subproblem 2
r + 144.4 = -167.286700009 Simplifying r + 144.4 = -167.286700009 Reorder the terms: 144.4 + r = -167.286700009 Solving 144.4 + r = -167.286700009 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-144.4' to each side of the equation. 144.4 + -144.4 + r = -167.286700009 + -144.4 Combine like terms: 144.4 + -144.4 = 0.0 0.0 + r = -167.286700009 + -144.4 r = -167.286700009 + -144.4 Combine like terms: -167.286700009 + -144.4 = -311.686700009 r = -311.686700009 Simplifying r = -311.686700009Solution
The solution to the problem is based on the solutions from the subproblems. r = {22.886700009, -311.686700009}
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