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Simplifying 3087.3736 = 3.14r2 + 2 * 3.14r * 99.9 Reorder the terms for easier multiplication: 3087.3736 = 3.14r2 + 2 * 3.14 * 99.9r Multiply 2 * 3.14 3087.3736 = 3.14r2 + 6.28 * 99.9r Multiply 6.28 * 99.9 3087.3736 = 3.14r2 + 627.372r Reorder the terms: 3087.3736 = 627.372r + 3.14r2 Solving 3087.3736 = 627.372r + 3.14r2 Solving for variable 'r'. Reorder the terms: 3087.3736 + -627.372r + -3.14r2 = 627.372r + -627.372r + 3.14r2 + -3.14r2 Combine like terms: 627.372r + -627.372r = 0.000 3087.3736 + -627.372r + -3.14r2 = 0.000 + 3.14r2 + -3.14r2 3087.3736 + -627.372r + -3.14r2 = 3.14r2 + -3.14r2 Combine like terms: 3.14r2 + -3.14r2 = 0.00 3087.3736 + -627.372r + -3.14r2 = 0.00 Begin completing the square. Divide all terms by -3.14 the coefficient of the squared term: Divide each side by '-3.14'. -983.24 + 199.8r + r2 = 0 Move the constant term to the right: Add '983.24' to each side of the equation. -983.24 + 199.8r + 983.24 + r2 = 0 + 983.24 Reorder the terms: -983.24 + 983.24 + 199.8r + r2 = 0 + 983.24 Combine like terms: -983.24 + 983.24 = 0.00 0.00 + 199.8r + r2 = 0 + 983.24 199.8r + r2 = 0 + 983.24 Combine like terms: 0 + 983.24 = 983.24 199.8r + r2 = 983.24 The r term is 199.8r. Take half its coefficient (99.9). Square it (9980.01) and add it to both sides. Add '9980.01' to each side of the equation. 199.8r + 9980.01 + r2 = 983.24 + 9980.01 Reorder the terms: 9980.01 + 199.8r + r2 = 983.24 + 9980.01 Combine like terms: 983.24 + 9980.01 = 10963.25 9980.01 + 199.8r + r2 = 10963.25 Factor a perfect square on the left side: (r + 99.9)(r + 99.9) = 10963.25 Calculate the square root of the right side: 104.705539491 Break this problem into two subproblems by setting (r + 99.9) equal to 104.705539491 and -104.705539491.Subproblem 1
r + 99.9 = 104.705539491 Simplifying r + 99.9 = 104.705539491 Reorder the terms: 99.9 + r = 104.705539491 Solving 99.9 + r = 104.705539491 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-99.9' to each side of the equation. 99.9 + -99.9 + r = 104.705539491 + -99.9 Combine like terms: 99.9 + -99.9 = 0.0 0.0 + r = 104.705539491 + -99.9 r = 104.705539491 + -99.9 Combine like terms: 104.705539491 + -99.9 = 4.805539491 r = 4.805539491 Simplifying r = 4.805539491Subproblem 2
r + 99.9 = -104.705539491 Simplifying r + 99.9 = -104.705539491 Reorder the terms: 99.9 + r = -104.705539491 Solving 99.9 + r = -104.705539491 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-99.9' to each side of the equation. 99.9 + -99.9 + r = -104.705539491 + -99.9 Combine like terms: 99.9 + -99.9 = 0.0 0.0 + r = -104.705539491 + -99.9 r = -104.705539491 + -99.9 Combine like terms: -104.705539491 + -99.9 = -204.605539491 r = -204.605539491 Simplifying r = -204.605539491Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.805539491, -204.605539491}
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