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Simplifying 25722.8 = 2 * 3.14r2 + 3.14r * 240 Multiply 2 * 3.14 25722.8 = 6.28r2 + 3.14r * 240 Reorder the terms for easier multiplication: 25722.8 = 6.28r2 + 3.14 * 240r Multiply 3.14 * 240 25722.8 = 6.28r2 + 753.6r Reorder the terms: 25722.8 = 753.6r + 6.28r2 Solving 25722.8 = 753.6r + 6.28r2 Solving for variable 'r'. Reorder the terms: 25722.8 + -753.6r + -6.28r2 = 753.6r + -753.6r + 6.28r2 + -6.28r2 Combine like terms: 753.6r + -753.6r = 0.0 25722.8 + -753.6r + -6.28r2 = 0.0 + 6.28r2 + -6.28r2 25722.8 + -753.6r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 25722.8 + -753.6r + -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'. -4095.987261 + 120r + r2 = 0 Move the constant term to the right: Add '4095.987261' to each side of the equation. -4095.987261 + 120r + 4095.987261 + r2 = 0 + 4095.987261 Reorder the terms: -4095.987261 + 4095.987261 + 120r + r2 = 0 + 4095.987261 Combine like terms: -4095.987261 + 4095.987261 = 0.000000 0.000000 + 120r + r2 = 0 + 4095.987261 120r + r2 = 0 + 4095.987261 Combine like terms: 0 + 4095.987261 = 4095.987261 120r + r2 = 4095.987261 The r term is 120r. Take half its coefficient (60). Square it (3600) and add it to both sides. Add '3600' to each side of the equation. 120r + 3600 + r2 = 4095.987261 + 3600 Reorder the terms: 3600 + 120r + r2 = 4095.987261 + 3600 Combine like terms: 4095.987261 + 3600 = 7695.987261 3600 + 120r + r2 = 7695.987261 Factor a perfect square on the left side: (r + 60)(r + 60) = 7695.987261 Calculate the square root of the right side: 87.726776192 Break this problem into two subproblems by setting (r + 60) equal to 87.726776192 and -87.726776192.Subproblem 1
r + 60 = 87.726776192 Simplifying r + 60 = 87.726776192 Reorder the terms: 60 + r = 87.726776192 Solving 60 + r = 87.726776192 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-60' to each side of the equation. 60 + -60 + r = 87.726776192 + -60 Combine like terms: 60 + -60 = 0 0 + r = 87.726776192 + -60 r = 87.726776192 + -60 Combine like terms: 87.726776192 + -60 = 27.726776192 r = 27.726776192 Simplifying r = 27.726776192Subproblem 2
r + 60 = -87.726776192 Simplifying r + 60 = -87.726776192 Reorder the terms: 60 + r = -87.726776192 Solving 60 + r = -87.726776192 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-60' to each side of the equation. 60 + -60 + r = -87.726776192 + -60 Combine like terms: 60 + -60 = 0 0 + r = -87.726776192 + -60 r = -87.726776192 + -60 Combine like terms: -87.726776192 + -60 = -147.726776192 r = -147.726776192 Simplifying r = -147.726776192Solution
The solution to the problem is based on the solutions from the subproblems. r = {27.726776192, -147.726776192}
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