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Simplifying 0 = 6.28r2 + 2028.44r + -47533.32 Reorder the terms: 0 = -47533.32 + 2028.44r + 6.28r2 Solving 0 = -47533.32 + 2028.44r + 6.28r2 Solving for variable 'r'. Combine like terms: 0 + 47533.32 = 47533.32 47533.32 + -2028.44r + -6.28r2 = -47533.32 + 2028.44r + 6.28r2 + 47533.32 + -2028.44r + -6.28r2 Reorder the terms: 47533.32 + -2028.44r + -6.28r2 = -47533.32 + 47533.32 + 2028.44r + -2028.44r + 6.28r2 + -6.28r2 Combine like terms: -47533.32 + 47533.32 = 0.00 47533.32 + -2028.44r + -6.28r2 = 0.00 + 2028.44r + -2028.44r + 6.28r2 + -6.28r2 47533.32 + -2028.44r + -6.28r2 = 2028.44r + -2028.44r + 6.28r2 + -6.28r2 Combine like terms: 2028.44r + -2028.44r = 0.00 47533.32 + -2028.44r + -6.28r2 = 0.00 + 6.28r2 + -6.28r2 47533.32 + -2028.44r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 47533.32 + -2028.44r + -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'. -7569 + 323r + r2 = 0 Move the constant term to the right: Add '7569' to each side of the equation. -7569 + 323r + 7569 + r2 = 0 + 7569 Reorder the terms: -7569 + 7569 + 323r + r2 = 0 + 7569 Combine like terms: -7569 + 7569 = 0 0 + 323r + r2 = 0 + 7569 323r + r2 = 0 + 7569 Combine like terms: 0 + 7569 = 7569 323r + r2 = 7569 The r term is 323r. Take half its coefficient (161.5). Square it (26082.25) and add it to both sides. Add '26082.25' to each side of the equation. 323r + 26082.25 + r2 = 7569 + 26082.25 Reorder the terms: 26082.25 + 323r + r2 = 7569 + 26082.25 Combine like terms: 7569 + 26082.25 = 33651.25 26082.25 + 323r + r2 = 33651.25 Factor a perfect square on the left side: (r + 161.5)(r + 161.5) = 33651.25 Calculate the square root of the right side: 183.442770367 Break this problem into two subproblems by setting (r + 161.5) equal to 183.442770367 and -183.442770367.Subproblem 1
r + 161.5 = 183.442770367 Simplifying r + 161.5 = 183.442770367 Reorder the terms: 161.5 + r = 183.442770367 Solving 161.5 + r = 183.442770367 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-161.5' to each side of the equation. 161.5 + -161.5 + r = 183.442770367 + -161.5 Combine like terms: 161.5 + -161.5 = 0.0 0.0 + r = 183.442770367 + -161.5 r = 183.442770367 + -161.5 Combine like terms: 183.442770367 + -161.5 = 21.942770367 r = 21.942770367 Simplifying r = 21.942770367Subproblem 2
r + 161.5 = -183.442770367 Simplifying r + 161.5 = -183.442770367 Reorder the terms: 161.5 + r = -183.442770367 Solving 161.5 + r = -183.442770367 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-161.5' to each side of the equation. 161.5 + -161.5 + r = -183.442770367 + -161.5 Combine like terms: 161.5 + -161.5 = 0.0 0.0 + r = -183.442770367 + -161.5 r = -183.442770367 + -161.5 Combine like terms: -183.442770367 + -161.5 = -344.942770367 r = -344.942770367 Simplifying r = -344.942770367Solution
The solution to the problem is based on the solutions from the subproblems. r = {21.942770367, -344.942770367}
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