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Simplifying -4.8475x2 + 264.664x + 16708.25 = 0 Reorder the terms: 16708.25 + 264.664x + -4.8475x2 = 0 Solving 16708.25 + 264.664x + -4.8475x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.8475 the coefficient of the squared term: Divide each side by '-4.8475'. -3446.776689 + -54.59804023x + x2 = 0 Move the constant term to the right: Add '3446.776689' to each side of the equation. -3446.776689 + -54.59804023x + 3446.776689 + x2 = 0 + 3446.776689 Reorder the terms: -3446.776689 + 3446.776689 + -54.59804023x + x2 = 0 + 3446.776689 Combine like terms: -3446.776689 + 3446.776689 = 0.000000 0.000000 + -54.59804023x + x2 = 0 + 3446.776689 -54.59804023x + x2 = 0 + 3446.776689 Combine like terms: 0 + 3446.776689 = 3446.776689 -54.59804023x + x2 = 3446.776689 The x term is -54.59804023x. Take half its coefficient (-27.29902012). Square it (745.2364995) and add it to both sides. Add '745.2364995' to each side of the equation. -54.59804023x + 745.2364995 + x2 = 3446.776689 + 745.2364995 Reorder the terms: 745.2364995 + -54.59804023x + x2 = 3446.776689 + 745.2364995 Combine like terms: 3446.776689 + 745.2364995 = 4192.0131885 745.2364995 + -54.59804023x + x2 = 4192.0131885 Factor a perfect square on the left side: (x + -27.29902012)(x + -27.29902012) = 4192.0131885 Calculate the square root of the right side: 64.745758073 Break this problem into two subproblems by setting (x + -27.29902012) equal to 64.745758073 and -64.745758073.Subproblem 1
x + -27.29902012 = 64.745758073 Simplifying x + -27.29902012 = 64.745758073 Reorder the terms: -27.29902012 + x = 64.745758073 Solving -27.29902012 + x = 64.745758073 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.29902012' to each side of the equation. -27.29902012 + 27.29902012 + x = 64.745758073 + 27.29902012 Combine like terms: -27.29902012 + 27.29902012 = 0.00000000 0.00000000 + x = 64.745758073 + 27.29902012 x = 64.745758073 + 27.29902012 Combine like terms: 64.745758073 + 27.29902012 = 92.044778193 x = 92.044778193 Simplifying x = 92.044778193Subproblem 2
x + -27.29902012 = -64.745758073 Simplifying x + -27.29902012 = -64.745758073 Reorder the terms: -27.29902012 + x = -64.745758073 Solving -27.29902012 + x = -64.745758073 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.29902012' to each side of the equation. -27.29902012 + 27.29902012 + x = -64.745758073 + 27.29902012 Combine like terms: -27.29902012 + 27.29902012 = 0.00000000 0.00000000 + x = -64.745758073 + 27.29902012 x = -64.745758073 + 27.29902012 Combine like terms: -64.745758073 + 27.29902012 = -37.446737953 x = -37.446737953 Simplifying x = -37.446737953Solution
The solution to the problem is based on the solutions from the subproblems. x = {92.044778193, -37.446737953}
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