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Simplifying 44798.2544 = 2 * 3.14r2 + 2 * 3.14r * 22.8 Multiply 2 * 3.14 44798.2544 = 6.28r2 + 2 * 3.14r * 22.8 Reorder the terms for easier multiplication: 44798.2544 = 6.28r2 + 2 * 3.14 * 22.8r Multiply 2 * 3.14 44798.2544 = 6.28r2 + 6.28 * 22.8r Multiply 6.28 * 22.8 44798.2544 = 6.28r2 + 143.184r Reorder the terms: 44798.2544 = 143.184r + 6.28r2 Solving 44798.2544 = 143.184r + 6.28r2 Solving for variable 'r'. Reorder the terms: 44798.2544 + -143.184r + -6.28r2 = 143.184r + -143.184r + 6.28r2 + -6.28r2 Combine like terms: 143.184r + -143.184r = 0.000 44798.2544 + -143.184r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2 44798.2544 + -143.184r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 44798.2544 + -143.184r + -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 + 22.8r + r2 = 0 Move the constant term to the right: Add '7133.48' to each side of the equation. -7133.48 + 22.8r + 7133.48 + r2 = 0 + 7133.48 Reorder the terms: -7133.48 + 7133.48 + 22.8r + r2 = 0 + 7133.48 Combine like terms: -7133.48 + 7133.48 = 0.00 0.00 + 22.8r + r2 = 0 + 7133.48 22.8r + r2 = 0 + 7133.48 Combine like terms: 0 + 7133.48 = 7133.48 22.8r + r2 = 7133.48 The r term is 22.8r. Take half its coefficient (11.4). Square it (129.96) and add it to both sides. Add '129.96' to each side of the equation. 22.8r + 129.96 + r2 = 7133.48 + 129.96 Reorder the terms: 129.96 + 22.8r + r2 = 7133.48 + 129.96 Combine like terms: 7133.48 + 129.96 = 7263.44 129.96 + 22.8r + r2 = 7263.44 Factor a perfect square on the left side: (r + 11.4)(r + 11.4) = 7263.44 Calculate the square root of the right side: 85.225817685 Break this problem into two subproblems by setting (r + 11.4) equal to 85.225817685 and -85.225817685.Subproblem 1
r + 11.4 = 85.225817685 Simplifying r + 11.4 = 85.225817685 Reorder the terms: 11.4 + r = 85.225817685 Solving 11.4 + r = 85.225817685 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-11.4' to each side of the equation. 11.4 + -11.4 + r = 85.225817685 + -11.4 Combine like terms: 11.4 + -11.4 = 0.0 0.0 + r = 85.225817685 + -11.4 r = 85.225817685 + -11.4 Combine like terms: 85.225817685 + -11.4 = 73.825817685 r = 73.825817685 Simplifying r = 73.825817685Subproblem 2
r + 11.4 = -85.225817685 Simplifying r + 11.4 = -85.225817685 Reorder the terms: 11.4 + r = -85.225817685 Solving 11.4 + r = -85.225817685 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-11.4' to each side of the equation. 11.4 + -11.4 + r = -85.225817685 + -11.4 Combine like terms: 11.4 + -11.4 = 0.0 0.0 + r = -85.225817685 + -11.4 r = -85.225817685 + -11.4 Combine like terms: -85.225817685 + -11.4 = -96.625817685 r = -96.625817685 Simplifying r = -96.625817685Solution
The solution to the problem is based on the solutions from the subproblems. r = {73.825817685, -96.625817685}
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