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Simplifying 2442.7316 = 2 * 3.14r2 + 2 * 3.14r * 30.4 Multiply 2 * 3.14 2442.7316 = 6.28r2 + 2 * 3.14r * 30.4 Reorder the terms for easier multiplication: 2442.7316 = 6.28r2 + 2 * 3.14 * 30.4r Multiply 2 * 3.14 2442.7316 = 6.28r2 + 6.28 * 30.4r Multiply 6.28 * 30.4 2442.7316 = 6.28r2 + 190.912r Reorder the terms: 2442.7316 = 190.912r + 6.28r2 Solving 2442.7316 = 190.912r + 6.28r2 Solving for variable 'r'. Reorder the terms: 2442.7316 + -190.912r + -6.28r2 = 190.912r + -190.912r + 6.28r2 + -6.28r2 Combine like terms: 190.912r + -190.912r = 0.000 2442.7316 + -190.912r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2 2442.7316 + -190.912r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 2442.7316 + -190.912r + -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'. -388.97 + 30.4r + r2 = 0 Move the constant term to the right: Add '388.97' to each side of the equation. -388.97 + 30.4r + 388.97 + r2 = 0 + 388.97 Reorder the terms: -388.97 + 388.97 + 30.4r + r2 = 0 + 388.97 Combine like terms: -388.97 + 388.97 = 0.00 0.00 + 30.4r + r2 = 0 + 388.97 30.4r + r2 = 0 + 388.97 Combine like terms: 0 + 388.97 = 388.97 30.4r + r2 = 388.97 The r term is 30.4r. Take half its coefficient (15.2). Square it (231.04) and add it to both sides. Add '231.04' to each side of the equation. 30.4r + 231.04 + r2 = 388.97 + 231.04 Reorder the terms: 231.04 + 30.4r + r2 = 388.97 + 231.04 Combine like terms: 388.97 + 231.04 = 620.01 231.04 + 30.4r + r2 = 620.01 Factor a perfect square on the left side: (r + 15.2)(r + 15.2) = 620.01 Calculate the square root of the right side: 24.9 Break this problem into two subproblems by setting (r + 15.2) equal to 24.9 and -24.9.Subproblem 1
r + 15.2 = 24.9 Simplifying r + 15.2 = 24.9 Reorder the terms: 15.2 + r = 24.9 Solving 15.2 + r = 24.9 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-15.2' to each side of the equation. 15.2 + -15.2 + r = 24.9 + -15.2 Combine like terms: 15.2 + -15.2 = 0.0 0.0 + r = 24.9 + -15.2 r = 24.9 + -15.2 Combine like terms: 24.9 + -15.2 = 9.7 r = 9.7 Simplifying r = 9.7Subproblem 2
r + 15.2 = -24.9 Simplifying r + 15.2 = -24.9 Reorder the terms: 15.2 + r = -24.9 Solving 15.2 + r = -24.9 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-15.2' to each side of the equation. 15.2 + -15.2 + r = -24.9 + -15.2 Combine like terms: 15.2 + -15.2 = 0.0 0.0 + r = -24.9 + -15.2 r = -24.9 + -15.2 Combine like terms: -24.9 + -15.2 = -40.1 r = -40.1 Simplifying r = -40.1Solution
The solution to the problem is based on the solutions from the subproblems. r = {9.7, -40.1}
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