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Simplifying 633024 = 6.28r2 + 101.736r Reorder the terms: 633024 = 101.736r + 6.28r2 Solving 633024 = 101.736r + 6.28r2 Solving for variable 'r'. Reorder the terms: 633024 + -101.736r + -6.28r2 = 101.736r + -101.736r + 6.28r2 + -6.28r2 Combine like terms: 101.736r + -101.736r = 0.000 633024 + -101.736r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2 633024 + -101.736r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 633024 + -101.736r + -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'. -100800 + 16.2r + r2 = 0 Move the constant term to the right: Add '100800' to each side of the equation. -100800 + 16.2r + 100800 + r2 = 0 + 100800 Reorder the terms: -100800 + 100800 + 16.2r + r2 = 0 + 100800 Combine like terms: -100800 + 100800 = 0 0 + 16.2r + r2 = 0 + 100800 16.2r + r2 = 0 + 100800 Combine like terms: 0 + 100800 = 100800 16.2r + r2 = 100800 The r term is 16.2r. Take half its coefficient (8.1). Square it (65.61) and add it to both sides. Add '65.61' to each side of the equation. 16.2r + 65.61 + r2 = 100800 + 65.61 Reorder the terms: 65.61 + 16.2r + r2 = 100800 + 65.61 Combine like terms: 100800 + 65.61 = 100865.61 65.61 + 16.2r + r2 = 100865.61 Factor a perfect square on the left side: (r + 8.1)(r + 8.1) = 100865.61 Calculate the square root of the right side: 317.593466557 Break this problem into two subproblems by setting (r + 8.1) equal to 317.593466557 and -317.593466557.Subproblem 1
r + 8.1 = 317.593466557 Simplifying r + 8.1 = 317.593466557 Reorder the terms: 8.1 + r = 317.593466557 Solving 8.1 + r = 317.593466557 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8.1' to each side of the equation. 8.1 + -8.1 + r = 317.593466557 + -8.1 Combine like terms: 8.1 + -8.1 = 0.0 0.0 + r = 317.593466557 + -8.1 r = 317.593466557 + -8.1 Combine like terms: 317.593466557 + -8.1 = 309.493466557 r = 309.493466557 Simplifying r = 309.493466557Subproblem 2
r + 8.1 = -317.593466557 Simplifying r + 8.1 = -317.593466557 Reorder the terms: 8.1 + r = -317.593466557 Solving 8.1 + r = -317.593466557 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8.1' to each side of the equation. 8.1 + -8.1 + r = -317.593466557 + -8.1 Combine like terms: 8.1 + -8.1 = 0.0 0.0 + r = -317.593466557 + -8.1 r = -317.593466557 + -8.1 Combine like terms: -317.593466557 + -8.1 = -325.693466557 r = -325.693466557 Simplifying r = -325.693466557Solution
The solution to the problem is based on the solutions from the subproblems. r = {309.493466557, -325.693466557}
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