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Simplifying 2400 = -0.598x2 + 97.750x + 664.870 Reorder the terms: 2400 = 664.870 + 97.750x + -0.598x2 Solving 2400 = 664.870 + 97.750x + -0.598x2 Solving for variable 'x'. Combine like terms: 2400 + -664.870 = 1735.13 1735.13 + -97.750x + 0.598x2 = 664.870 + 97.750x + -0.598x2 + -664.870 + -97.750x + 0.598x2 Reorder the terms: 1735.13 + -97.750x + 0.598x2 = 664.870 + -664.870 + 97.750x + -97.750x + -0.598x2 + 0.598x2 Combine like terms: 664.870 + -664.870 = 0.000 1735.13 + -97.750x + 0.598x2 = 0.000 + 97.750x + -97.750x + -0.598x2 + 0.598x2 1735.13 + -97.750x + 0.598x2 = 97.750x + -97.750x + -0.598x2 + 0.598x2 Combine like terms: 97.750x + -97.750x = 0.000 1735.13 + -97.750x + 0.598x2 = 0.000 + -0.598x2 + 0.598x2 1735.13 + -97.750x + 0.598x2 = -0.598x2 + 0.598x2 Combine like terms: -0.598x2 + 0.598x2 = 0.000 1735.13 + -97.750x + 0.598x2 = 0.000 Begin completing the square. Divide all terms by 0.598 the coefficient of the squared term: Divide each side by '0.598'. 2901.555184 + -163.4615385x + x2 = 0 Move the constant term to the right: Add '-2901.555184' to each side of the equation. 2901.555184 + -163.4615385x + -2901.555184 + x2 = 0 + -2901.555184 Reorder the terms: 2901.555184 + -2901.555184 + -163.4615385x + x2 = 0 + -2901.555184 Combine like terms: 2901.555184 + -2901.555184 = 0.000000 0.000000 + -163.4615385x + x2 = 0 + -2901.555184 -163.4615385x + x2 = 0 + -2901.555184 Combine like terms: 0 + -2901.555184 = -2901.555184 -163.4615385x + x2 = -2901.555184 The x term is -163.4615385x. Take half its coefficient (-81.73076925). Square it (6679.918642) and add it to both sides. Add '6679.918642' to each side of the equation. -163.4615385x + 6679.918642 + x2 = -2901.555184 + 6679.918642 Reorder the terms: 6679.918642 + -163.4615385x + x2 = -2901.555184 + 6679.918642 Combine like terms: -2901.555184 + 6679.918642 = 3778.363458 6679.918642 + -163.4615385x + x2 = 3778.363458 Factor a perfect square on the left side: (x + -81.73076925)(x + -81.73076925) = 3778.363458 Calculate the square root of the right side: 61.468393976 Break this problem into two subproblems by setting (x + -81.73076925) equal to 61.468393976 and -61.468393976.Subproblem 1
x + -81.73076925 = 61.468393976 Simplifying x + -81.73076925 = 61.468393976 Reorder the terms: -81.73076925 + x = 61.468393976 Solving -81.73076925 + x = 61.468393976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '81.73076925' to each side of the equation. -81.73076925 + 81.73076925 + x = 61.468393976 + 81.73076925 Combine like terms: -81.73076925 + 81.73076925 = 0.00000000 0.00000000 + x = 61.468393976 + 81.73076925 x = 61.468393976 + 81.73076925 Combine like terms: 61.468393976 + 81.73076925 = 143.199163226 x = 143.199163226 Simplifying x = 143.199163226Subproblem 2
x + -81.73076925 = -61.468393976 Simplifying x + -81.73076925 = -61.468393976 Reorder the terms: -81.73076925 + x = -61.468393976 Solving -81.73076925 + x = -61.468393976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '81.73076925' to each side of the equation. -81.73076925 + 81.73076925 + x = -61.468393976 + 81.73076925 Combine like terms: -81.73076925 + 81.73076925 = 0.00000000 0.00000000 + x = -61.468393976 + 81.73076925 x = -61.468393976 + 81.73076925 Combine like terms: -61.468393976 + 81.73076925 = 20.262375274 x = 20.262375274 Simplifying x = 20.262375274Solution
The solution to the problem is based on the solutions from the subproblems. x = {143.199163226, 20.262375274}
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