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Simplifying 9653616 = 2 * 3.14r2 + 2 * 3.14r * 9.9 Multiply 2 * 3.14 9653616 = 6.28r2 + 2 * 3.14r * 9.9 Reorder the terms for easier multiplication: 9653616 = 6.28r2 + 2 * 3.14 * 9.9r Multiply 2 * 3.14 9653616 = 6.28r2 + 6.28 * 9.9r Multiply 6.28 * 9.9 9653616 = 6.28r2 + 62.172r Reorder the terms: 9653616 = 62.172r + 6.28r2 Solving 9653616 = 62.172r + 6.28r2 Solving for variable 'r'. Reorder the terms: 9653616 + -62.172r + -6.28r2 = 62.172r + -62.172r + 6.28r2 + -6.28r2 Combine like terms: 62.172r + -62.172r = 0.000 9653616 + -62.172r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2 9653616 + -62.172r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 9653616 + -62.172r + -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'. -1537200 + 9.9r + r2 = 0 Move the constant term to the right: Add '1537200' to each side of the equation. -1537200 + 9.9r + 1537200 + r2 = 0 + 1537200 Reorder the terms: -1537200 + 1537200 + 9.9r + r2 = 0 + 1537200 Combine like terms: -1537200 + 1537200 = 0 0 + 9.9r + r2 = 0 + 1537200 9.9r + r2 = 0 + 1537200 Combine like terms: 0 + 1537200 = 1537200 9.9r + r2 = 1537200 The r term is 9.9r. Take half its coefficient (4.95). Square it (24.5025) and add it to both sides. Add '24.5025' to each side of the equation. 9.9r + 24.5025 + r2 = 1537200 + 24.5025 Reorder the terms: 24.5025 + 9.9r + r2 = 1537200 + 24.5025 Combine like terms: 1537200 + 24.5025 = 1537224.5025 24.5025 + 9.9r + r2 = 1537224.5025 Factor a perfect square on the left side: (r + 4.95)(r + 4.95) = 1537224.5025 Calculate the square root of the right side: 1239.848580473 Break this problem into two subproblems by setting (r + 4.95) equal to 1239.848580473 and -1239.848580473.Subproblem 1
r + 4.95 = 1239.848580473 Simplifying r + 4.95 = 1239.848580473 Reorder the terms: 4.95 + r = 1239.848580473 Solving 4.95 + r = 1239.848580473 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4.95' to each side of the equation. 4.95 + -4.95 + r = 1239.848580473 + -4.95 Combine like terms: 4.95 + -4.95 = 0.00 0.00 + r = 1239.848580473 + -4.95 r = 1239.848580473 + -4.95 Combine like terms: 1239.848580473 + -4.95 = 1234.898580473 r = 1234.898580473 Simplifying r = 1234.898580473Subproblem 2
r + 4.95 = -1239.848580473 Simplifying r + 4.95 = -1239.848580473 Reorder the terms: 4.95 + r = -1239.848580473 Solving 4.95 + r = -1239.848580473 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4.95' to each side of the equation. 4.95 + -4.95 + r = -1239.848580473 + -4.95 Combine like terms: 4.95 + -4.95 = 0.00 0.00 + r = -1239.848580473 + -4.95 r = -1239.848580473 + -4.95 Combine like terms: -1239.848580473 + -4.95 = -1244.798580473 r = -1244.798580473 Simplifying r = -1244.798580473Solution
The solution to the problem is based on the solutions from the subproblems. r = {1234.898580473, -1244.798580473}
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