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Simplifying -3.5x2 + 3775x + -135732.5 = 0 Reorder the terms: -135732.5 + 3775x + -3.5x2 = 0 Solving -135732.5 + 3775x + -3.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3.5 the coefficient of the squared term: Divide each side by '-3.5'. 38780.71429 + -1078.571429x + x2 = 0 Move the constant term to the right: Add '-38780.71429' to each side of the equation. 38780.71429 + -1078.571429x + -38780.71429 + x2 = 0 + -38780.71429 Reorder the terms: 38780.71429 + -38780.71429 + -1078.571429x + x2 = 0 + -38780.71429 Combine like terms: 38780.71429 + -38780.71429 = 0.00000 0.00000 + -1078.571429x + x2 = 0 + -38780.71429 -1078.571429x + x2 = 0 + -38780.71429 Combine like terms: 0 + -38780.71429 = -38780.71429 -1078.571429x + x2 = -38780.71429 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 = -38780.71429 + 290829.0819 Reorder the terms: 290829.0819 + -1078.571429x + x2 = -38780.71429 + 290829.0819 Combine like terms: -38780.71429 + 290829.0819 = 252048.36761 290829.0819 + -1078.571429x + x2 = 252048.36761 Factor a perfect square on the left side: (x + -539.2857145)(x + -539.2857145) = 252048.36761 Calculate the square root of the right side: 502.044188902 Break this problem into two subproblems by setting (x + -539.2857145) equal to 502.044188902 and -502.044188902.Subproblem 1
x + -539.2857145 = 502.044188902 Simplifying x + -539.2857145 = 502.044188902 Reorder the terms: -539.2857145 + x = 502.044188902 Solving -539.2857145 + x = 502.044188902 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 = 502.044188902 + 539.2857145 Combine like terms: -539.2857145 + 539.2857145 = 0.0000000 0.0000000 + x = 502.044188902 + 539.2857145 x = 502.044188902 + 539.2857145 Combine like terms: 502.044188902 + 539.2857145 = 1041.329903402 x = 1041.329903402 Simplifying x = 1041.329903402Subproblem 2
x + -539.2857145 = -502.044188902 Simplifying x + -539.2857145 = -502.044188902 Reorder the terms: -539.2857145 + x = -502.044188902 Solving -539.2857145 + x = -502.044188902 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 = -502.044188902 + 539.2857145 Combine like terms: -539.2857145 + 539.2857145 = 0.0000000 0.0000000 + x = -502.044188902 + 539.2857145 x = -502.044188902 + 539.2857145 Combine like terms: -502.044188902 + 539.2857145 = 37.241525598 x = 37.241525598 Simplifying x = 37.241525598Solution
The solution to the problem is based on the solutions from the subproblems. x = {1041.329903402, 37.241525598}
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