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Simplifying 650000 = -3.5x2 + 3775x + -135732.5 Reorder the terms: 650000 = -135732.5 + 3775x + -3.5x2 Solving 650000 = -135732.5 + 3775x + -3.5x2 Solving for variable 'x'. Combine like terms: 650000 + 135732.5 = 785732.5 785732.5 + -3775x + 3.5x2 = -135732.5 + 3775x + -3.5x2 + 135732.5 + -3775x + 3.5x2 Reorder the terms: 785732.5 + -3775x + 3.5x2 = -135732.5 + 135732.5 + 3775x + -3775x + -3.5x2 + 3.5x2 Combine like terms: -135732.5 + 135732.5 = 0.0 785732.5 + -3775x + 3.5x2 = 0.0 + 3775x + -3775x + -3.5x2 + 3.5x2 785732.5 + -3775x + 3.5x2 = 3775x + -3775x + -3.5x2 + 3.5x2 Combine like terms: 3775x + -3775x = 0 785732.5 + -3775x + 3.5x2 = 0 + -3.5x2 + 3.5x2 785732.5 + -3775x + 3.5x2 = -3.5x2 + 3.5x2 Combine like terms: -3.5x2 + 3.5x2 = 0.0 785732.5 + -3775x + 3.5x2 = 0.0 Begin completing the square. Divide all terms by 3.5 the coefficient of the squared term: Divide each side by '3.5'. 224495 + -1078.571429x + x2 = 0 Move the constant term to the right: Add '-224495' to each side of the equation. 224495 + -1078.571429x + -224495 + x2 = 0 + -224495 Reorder the terms: 224495 + -224495 + -1078.571429x + x2 = 0 + -224495 Combine like terms: 224495 + -224495 = 0 0 + -1078.571429x + x2 = 0 + -224495 -1078.571429x + x2 = 0 + -224495 Combine like terms: 0 + -224495 = -224495 -1078.571429x + x2 = -224495 The x term is -1078.571429x. Take half its coefficient (-539.2857145). Square it (290829.0819) and add it to both sides. Add '290829.0819' to each side of the equation. -1078.571429x + 290829.0819 + x2 = -224495 + 290829.0819 Reorder the terms: 290829.0819 + -1078.571429x + x2 = -224495 + 290829.0819 Combine like terms: -224495 + 290829.0819 = 66334.0819 290829.0819 + -1078.571429x + x2 = 66334.0819 Factor a perfect square on the left side: (x + -539.2857145)(x + -539.2857145) = 66334.0819 Calculate the square root of the right side: 257.554036854 Break this problem into two subproblems by setting (x + -539.2857145) equal to 257.554036854 and -257.554036854.Subproblem 1
x + -539.2857145 = 257.554036854 Simplifying x + -539.2857145 = 257.554036854 Reorder the terms: -539.2857145 + x = 257.554036854 Solving -539.2857145 + x = 257.554036854 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '539.2857145' to each side of the equation. -539.2857145 + 539.2857145 + x = 257.554036854 + 539.2857145 Combine like terms: -539.2857145 + 539.2857145 = 0.0000000 0.0000000 + x = 257.554036854 + 539.2857145 x = 257.554036854 + 539.2857145 Combine like terms: 257.554036854 + 539.2857145 = 796.839751354 x = 796.839751354 Simplifying x = 796.839751354Subproblem 2
x + -539.2857145 = -257.554036854 Simplifying x + -539.2857145 = -257.554036854 Reorder the terms: -539.2857145 + x = -257.554036854 Solving -539.2857145 + x = -257.554036854 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '539.2857145' to each side of the equation. -539.2857145 + 539.2857145 + x = -257.554036854 + 539.2857145 Combine like terms: -539.2857145 + 539.2857145 = 0.0000000 0.0000000 + x = -257.554036854 + 539.2857145 x = -257.554036854 + 539.2857145 Combine like terms: -257.554036854 + 539.2857145 = 281.731677646 x = 281.731677646 Simplifying x = 281.731677646Solution
The solution to the problem is based on the solutions from the subproblems. x = {796.839751354, 281.731677646}
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