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Simplifying 3150.048 = 2 * 3.14r * r + 3 * 3.14r * 99.7 Multiply 2 * 3.14 3150.048 = 6.28r * r + 3 * 3.14r * 99.7 Multiply r * r 3150.048 = 6.28r2 + 3 * 3.14r * 99.7 Reorder the terms for easier multiplication: 3150.048 = 6.28r2 + 3 * 3.14 * 99.7r Multiply 3 * 3.14 3150.048 = 6.28r2 + 9.42 * 99.7r Multiply 9.42 * 99.7 3150.048 = 6.28r2 + 939.174r Reorder the terms: 3150.048 = 939.174r + 6.28r2 Solving 3150.048 = 939.174r + 6.28r2 Solving for variable 'r'. Reorder the terms: 3150.048 + -939.174r + -6.28r2 = 939.174r + -939.174r + 6.28r2 + -6.28r2 Combine like terms: 939.174r + -939.174r = 0.000 3150.048 + -939.174r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2 3150.048 + -939.174r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 3150.048 + -939.174r + -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'. -501.6 + 149.55r + r2 = 0 Move the constant term to the right: Add '501.6' to each side of the equation. -501.6 + 149.55r + 501.6 + r2 = 0 + 501.6 Reorder the terms: -501.6 + 501.6 + 149.55r + r2 = 0 + 501.6 Combine like terms: -501.6 + 501.6 = 0.0 0.0 + 149.55r + r2 = 0 + 501.6 149.55r + r2 = 0 + 501.6 Combine like terms: 0 + 501.6 = 501.6 149.55r + r2 = 501.6 The r term is 149.55r. Take half its coefficient (74.775). Square it (5591.300625) and add it to both sides. Add '5591.300625' to each side of the equation. 149.55r + 5591.300625 + r2 = 501.6 + 5591.300625 Reorder the terms: 5591.300625 + 149.55r + r2 = 501.6 + 5591.300625 Combine like terms: 501.6 + 5591.300625 = 6092.900625 5591.300625 + 149.55r + r2 = 6092.900625 Factor a perfect square on the left side: (r + 74.775)(r + 74.775) = 6092.900625 Calculate the square root of the right side: 78.057034436 Break this problem into two subproblems by setting (r + 74.775) equal to 78.057034436 and -78.057034436.Subproblem 1
r + 74.775 = 78.057034436 Simplifying r + 74.775 = 78.057034436 Reorder the terms: 74.775 + r = 78.057034436 Solving 74.775 + r = 78.057034436 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-74.775' to each side of the equation. 74.775 + -74.775 + r = 78.057034436 + -74.775 Combine like terms: 74.775 + -74.775 = 0.000 0.000 + r = 78.057034436 + -74.775 r = 78.057034436 + -74.775 Combine like terms: 78.057034436 + -74.775 = 3.282034436 r = 3.282034436 Simplifying r = 3.282034436Subproblem 2
r + 74.775 = -78.057034436 Simplifying r + 74.775 = -78.057034436 Reorder the terms: 74.775 + r = -78.057034436 Solving 74.775 + r = -78.057034436 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-74.775' to each side of the equation. 74.775 + -74.775 + r = -78.057034436 + -74.775 Combine like terms: 74.775 + -74.775 = 0.000 0.000 + r = -78.057034436 + -74.775 r = -78.057034436 + -74.775 Combine like terms: -78.057034436 + -74.775 = -152.832034436 r = -152.832034436 Simplifying r = -152.832034436Solution
The solution to the problem is based on the solutions from the subproblems. r = {3.282034436, -152.832034436}
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