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Simplifying 4x2 + -145x + -4750 = 0 Reorder the terms: -4750 + -145x + 4x2 = 0 Solving -4750 + -145x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1187.5 + -36.25x + x2 = 0 Move the constant term to the right: Add '1187.5' to each side of the equation. -1187.5 + -36.25x + 1187.5 + x2 = 0 + 1187.5 Reorder the terms: -1187.5 + 1187.5 + -36.25x + x2 = 0 + 1187.5 Combine like terms: -1187.5 + 1187.5 = 0.0 0.0 + -36.25x + x2 = 0 + 1187.5 -36.25x + x2 = 0 + 1187.5 Combine like terms: 0 + 1187.5 = 1187.5 -36.25x + x2 = 1187.5 The x term is -36.25x. Take half its coefficient (-18.125). Square it (328.515625) and add it to both sides. Add '328.515625' to each side of the equation. -36.25x + 328.515625 + x2 = 1187.5 + 328.515625 Reorder the terms: 328.515625 + -36.25x + x2 = 1187.5 + 328.515625 Combine like terms: 1187.5 + 328.515625 = 1516.015625 328.515625 + -36.25x + x2 = 1516.015625 Factor a perfect square on the left side: (x + -18.125)(x + -18.125) = 1516.015625 Calculate the square root of the right side: 38.936045318 Break this problem into two subproblems by setting (x + -18.125) equal to 38.936045318 and -38.936045318.Subproblem 1
x + -18.125 = 38.936045318 Simplifying x + -18.125 = 38.936045318 Reorder the terms: -18.125 + x = 38.936045318 Solving -18.125 + x = 38.936045318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.125' to each side of the equation. -18.125 + 18.125 + x = 38.936045318 + 18.125 Combine like terms: -18.125 + 18.125 = 0.000 0.000 + x = 38.936045318 + 18.125 x = 38.936045318 + 18.125 Combine like terms: 38.936045318 + 18.125 = 57.061045318 x = 57.061045318 Simplifying x = 57.061045318Subproblem 2
x + -18.125 = -38.936045318 Simplifying x + -18.125 = -38.936045318 Reorder the terms: -18.125 + x = -38.936045318 Solving -18.125 + x = -38.936045318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.125' to each side of the equation. -18.125 + 18.125 + x = -38.936045318 + 18.125 Combine like terms: -18.125 + 18.125 = 0.000 0.000 + x = -38.936045318 + 18.125 x = -38.936045318 + 18.125 Combine like terms: -38.936045318 + 18.125 = -20.811045318 x = -20.811045318 Simplifying x = -20.811045318Solution
The solution to the problem is based on the solutions from the subproblems. x = {57.061045318, -20.811045318}
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