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Simplifying 3087.3736 = 2 * 3.14r2 + 2 * 3.14r * 99.9 Multiply 2 * 3.14 3087.3736 = 6.28r2 + 2 * 3.14r * 99.9 Reorder the terms for easier multiplication: 3087.3736 = 6.28r2 + 2 * 3.14 * 99.9r Multiply 2 * 3.14 3087.3736 = 6.28r2 + 6.28 * 99.9r Multiply 6.28 * 99.9 3087.3736 = 6.28r2 + 627.372r Reorder the terms: 3087.3736 = 627.372r + 6.28r2 Solving 3087.3736 = 627.372r + 6.28r2 Solving for variable 'r'. Reorder the terms: 3087.3736 + -627.372r + -6.28r2 = 627.372r + -627.372r + 6.28r2 + -6.28r2 Combine like terms: 627.372r + -627.372r = 0.000 3087.3736 + -627.372r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2 3087.3736 + -627.372r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 3087.3736 + -627.372r + -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'. -491.62 + 99.9r + r2 = 0 Move the constant term to the right: Add '491.62' to each side of the equation. -491.62 + 99.9r + 491.62 + r2 = 0 + 491.62 Reorder the terms: -491.62 + 491.62 + 99.9r + r2 = 0 + 491.62 Combine like terms: -491.62 + 491.62 = 0.00 0.00 + 99.9r + r2 = 0 + 491.62 99.9r + r2 = 0 + 491.62 Combine like terms: 0 + 491.62 = 491.62 99.9r + r2 = 491.62 The r term is 99.9r. Take half its coefficient (49.95). Square it (2495.0025) and add it to both sides. Add '2495.0025' to each side of the equation. 99.9r + 2495.0025 + r2 = 491.62 + 2495.0025 Reorder the terms: 2495.0025 + 99.9r + r2 = 491.62 + 2495.0025 Combine like terms: 491.62 + 2495.0025 = 2986.6225 2495.0025 + 99.9r + r2 = 2986.6225 Factor a perfect square on the left side: (r + 49.95)(r + 49.95) = 2986.6225 Calculate the square root of the right side: 54.65 Break this problem into two subproblems by setting (r + 49.95) equal to 54.65 and -54.65.Subproblem 1
r + 49.95 = 54.65 Simplifying r + 49.95 = 54.65 Reorder the terms: 49.95 + r = 54.65 Solving 49.95 + r = 54.65 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-49.95' to each side of the equation. 49.95 + -49.95 + r = 54.65 + -49.95 Combine like terms: 49.95 + -49.95 = 0.00 0.00 + r = 54.65 + -49.95 r = 54.65 + -49.95 Combine like terms: 54.65 + -49.95 = 4.7 r = 4.7 Simplifying r = 4.7Subproblem 2
r + 49.95 = -54.65 Simplifying r + 49.95 = -54.65 Reorder the terms: 49.95 + r = -54.65 Solving 49.95 + r = -54.65 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-49.95' to each side of the equation. 49.95 + -49.95 + r = -54.65 + -49.95 Combine like terms: 49.95 + -49.95 = 0.00 0.00 + r = -54.65 + -49.95 r = -54.65 + -49.95 Combine like terms: -54.65 + -49.95 = -104.6 r = -104.6 Simplifying r = -104.6Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.7, -104.6}
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