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Simplifying 2x2 + -240x + 5500 = x Reorder the terms: 5500 + -240x + 2x2 = x Solving 5500 + -240x + 2x2 = x Solving for variable 'x'. Reorder the terms: 5500 + -240x + -1x + 2x2 = x + -1x Combine like terms: -240x + -1x = -241x 5500 + -241x + 2x2 = x + -1x Combine like terms: x + -1x = 0 5500 + -241x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2750 + -120.5x + x2 = 0 Move the constant term to the right: Add '-2750' to each side of the equation. 2750 + -120.5x + -2750 + x2 = 0 + -2750 Reorder the terms: 2750 + -2750 + -120.5x + x2 = 0 + -2750 Combine like terms: 2750 + -2750 = 0 0 + -120.5x + x2 = 0 + -2750 -120.5x + x2 = 0 + -2750 Combine like terms: 0 + -2750 = -2750 -120.5x + x2 = -2750 The x term is -120.5x. Take half its coefficient (-60.25). Square it (3630.0625) and add it to both sides. Add '3630.0625' to each side of the equation. -120.5x + 3630.0625 + x2 = -2750 + 3630.0625 Reorder the terms: 3630.0625 + -120.5x + x2 = -2750 + 3630.0625 Combine like terms: -2750 + 3630.0625 = 880.0625 3630.0625 + -120.5x + x2 = 880.0625 Factor a perfect square on the left side: (x + -60.25)(x + -60.25) = 880.0625 Calculate the square root of the right side: 29.665847367 Break this problem into two subproblems by setting (x + -60.25) equal to 29.665847367 and -29.665847367.Subproblem 1
x + -60.25 = 29.665847367 Simplifying x + -60.25 = 29.665847367 Reorder the terms: -60.25 + x = 29.665847367 Solving -60.25 + x = 29.665847367 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60.25' to each side of the equation. -60.25 + 60.25 + x = 29.665847367 + 60.25 Combine like terms: -60.25 + 60.25 = 0.00 0.00 + x = 29.665847367 + 60.25 x = 29.665847367 + 60.25 Combine like terms: 29.665847367 + 60.25 = 89.915847367 x = 89.915847367 Simplifying x = 89.915847367Subproblem 2
x + -60.25 = -29.665847367 Simplifying x + -60.25 = -29.665847367 Reorder the terms: -60.25 + x = -29.665847367 Solving -60.25 + x = -29.665847367 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60.25' to each side of the equation. -60.25 + 60.25 + x = -29.665847367 + 60.25 Combine like terms: -60.25 + 60.25 = 0.00 0.00 + x = -29.665847367 + 60.25 x = -29.665847367 + 60.25 Combine like terms: -29.665847367 + 60.25 = 30.584152633 x = 30.584152633 Simplifying x = 30.584152633Solution
The solution to the problem is based on the solutions from the subproblems. x = {89.915847367, 30.584152633}
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