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Simplifying -0.028x2 + 4.578x + -170 = 0 Reorder the terms: -170 + 4.578x + -0.028x2 = 0 Solving -170 + 4.578x + -0.028x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.028 the coefficient of the squared term: Divide each side by '-0.028'. 6071.428571 + -163.5x + x2 = 0 Move the constant term to the right: Add '-6071.428571' to each side of the equation. 6071.428571 + -163.5x + -6071.428571 + x2 = 0 + -6071.428571 Reorder the terms: 6071.428571 + -6071.428571 + -163.5x + x2 = 0 + -6071.428571 Combine like terms: 6071.428571 + -6071.428571 = 0.000000 0.000000 + -163.5x + x2 = 0 + -6071.428571 -163.5x + x2 = 0 + -6071.428571 Combine like terms: 0 + -6071.428571 = -6071.428571 -163.5x + x2 = -6071.428571 The x term is -163.5x. Take half its coefficient (-81.75). Square it (6683.0625) and add it to both sides. Add '6683.0625' to each side of the equation. -163.5x + 6683.0625 + x2 = -6071.428571 + 6683.0625 Reorder the terms: 6683.0625 + -163.5x + x2 = -6071.428571 + 6683.0625 Combine like terms: -6071.428571 + 6683.0625 = 611.633929 6683.0625 + -163.5x + x2 = 611.633929 Factor a perfect square on the left side: (x + -81.75)(x + -81.75) = 611.633929 Calculate the square root of the right side: 24.731233875 Break this problem into two subproblems by setting (x + -81.75) equal to 24.731233875 and -24.731233875.Subproblem 1
x + -81.75 = 24.731233875 Simplifying x + -81.75 = 24.731233875 Reorder the terms: -81.75 + x = 24.731233875 Solving -81.75 + x = 24.731233875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '81.75' to each side of the equation. -81.75 + 81.75 + x = 24.731233875 + 81.75 Combine like terms: -81.75 + 81.75 = 0.00 0.00 + x = 24.731233875 + 81.75 x = 24.731233875 + 81.75 Combine like terms: 24.731233875 + 81.75 = 106.481233875 x = 106.481233875 Simplifying x = 106.481233875Subproblem 2
x + -81.75 = -24.731233875 Simplifying x + -81.75 = -24.731233875 Reorder the terms: -81.75 + x = -24.731233875 Solving -81.75 + x = -24.731233875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '81.75' to each side of the equation. -81.75 + 81.75 + x = -24.731233875 + 81.75 Combine like terms: -81.75 + 81.75 = 0.00 0.00 + x = -24.731233875 + 81.75 x = -24.731233875 + 81.75 Combine like terms: -24.731233875 + 81.75 = 57.018766125 x = 57.018766125 Simplifying x = 57.018766125Solution
The solution to the problem is based on the solutions from the subproblems. x = {106.481233875, 57.018766125}
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