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Simplifying -2.4x2 + -1x + 457 = 0 Reorder the terms: 457 + -1x + -2.4x2 = 0 Solving 457 + -1x + -2.4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2.4 the coefficient of the squared term: Divide each side by '-2.4'. -190.4166667 + 0.4166666667x + x2 = 0 Move the constant term to the right: Add '190.4166667' to each side of the equation. -190.4166667 + 0.4166666667x + 190.4166667 + x2 = 0 + 190.4166667 Reorder the terms: -190.4166667 + 190.4166667 + 0.4166666667x + x2 = 0 + 190.4166667 Combine like terms: -190.4166667 + 190.4166667 = 0.0000000 0.0000000 + 0.4166666667x + x2 = 0 + 190.4166667 0.4166666667x + x2 = 0 + 190.4166667 Combine like terms: 0 + 190.4166667 = 190.4166667 0.4166666667x + x2 = 190.4166667 The x term is 0.4166666667x. Take half its coefficient (0.2083333334). Square it (0.04340277781) and add it to both sides. Add '0.04340277781' to each side of the equation. 0.4166666667x + 0.04340277781 + x2 = 190.4166667 + 0.04340277781 Reorder the terms: 0.04340277781 + 0.4166666667x + x2 = 190.4166667 + 0.04340277781 Combine like terms: 190.4166667 + 0.04340277781 = 190.46006947781 0.04340277781 + 0.4166666667x + x2 = 190.46006947781 Factor a perfect square on the left side: (x + 0.2083333334)(x + 0.2083333334) = 190.46006947781 Calculate the square root of the right side: 13.800727136 Break this problem into two subproblems by setting (x + 0.2083333334) equal to 13.800727136 and -13.800727136.Subproblem 1
x + 0.2083333334 = 13.800727136 Simplifying x + 0.2083333334 = 13.800727136 Reorder the terms: 0.2083333334 + x = 13.800727136 Solving 0.2083333334 + x = 13.800727136 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + x = 13.800727136 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = 13.800727136 + -0.2083333334 x = 13.800727136 + -0.2083333334 Combine like terms: 13.800727136 + -0.2083333334 = 13.5923938026 x = 13.5923938026 Simplifying x = 13.5923938026Subproblem 2
x + 0.2083333334 = -13.800727136 Simplifying x + 0.2083333334 = -13.800727136 Reorder the terms: 0.2083333334 + x = -13.800727136 Solving 0.2083333334 + x = -13.800727136 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + x = -13.800727136 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = -13.800727136 + -0.2083333334 x = -13.800727136 + -0.2083333334 Combine like terms: -13.800727136 + -0.2083333334 = -14.0090604694 x = -14.0090604694 Simplifying x = -14.0090604694Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.5923938026, -14.0090604694}
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