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Simplifying -0.08769x2 + 1.7269x + 2 = 0 Reorder the terms: 2 + 1.7269x + -0.08769x2 = 0 Solving 2 + 1.7269x + -0.08769x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.08769 the coefficient of the squared term: Divide each side by '-0.08769'. -22.80761774 + -19.69323754x + x2 = 0 Move the constant term to the right: Add '22.80761774' to each side of the equation. -22.80761774 + -19.69323754x + 22.80761774 + x2 = 0 + 22.80761774 Reorder the terms: -22.80761774 + 22.80761774 + -19.69323754x + x2 = 0 + 22.80761774 Combine like terms: -22.80761774 + 22.80761774 = 0.00000000 0.00000000 + -19.69323754x + x2 = 0 + 22.80761774 -19.69323754x + x2 = 0 + 22.80761774 Combine like terms: 0 + 22.80761774 = 22.80761774 -19.69323754x + x2 = 22.80761774 The x term is -19.69323754x. Take half its coefficient (-9.84661877). Square it (96.95590120) and add it to both sides. Add '96.95590120' to each side of the equation. -19.69323754x + 96.95590120 + x2 = 22.80761774 + 96.95590120 Reorder the terms: 96.95590120 + -19.69323754x + x2 = 22.80761774 + 96.95590120 Combine like terms: 22.80761774 + 96.95590120 = 119.76351894 96.95590120 + -19.69323754x + x2 = 119.76351894 Factor a perfect square on the left side: (x + -9.84661877)(x + -9.84661877) = 119.76351894 Calculate the square root of the right side: 10.943651993 Break this problem into two subproblems by setting (x + -9.84661877) equal to 10.943651993 and -10.943651993.Subproblem 1
x + -9.84661877 = 10.943651993 Simplifying x + -9.84661877 = 10.943651993 Reorder the terms: -9.84661877 + x = 10.943651993 Solving -9.84661877 + x = 10.943651993 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.84661877' to each side of the equation. -9.84661877 + 9.84661877 + x = 10.943651993 + 9.84661877 Combine like terms: -9.84661877 + 9.84661877 = 0.00000000 0.00000000 + x = 10.943651993 + 9.84661877 x = 10.943651993 + 9.84661877 Combine like terms: 10.943651993 + 9.84661877 = 20.790270763 x = 20.790270763 Simplifying x = 20.790270763Subproblem 2
x + -9.84661877 = -10.943651993 Simplifying x + -9.84661877 = -10.943651993 Reorder the terms: -9.84661877 + x = -10.943651993 Solving -9.84661877 + x = -10.943651993 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.84661877' to each side of the equation. -9.84661877 + 9.84661877 + x = -10.943651993 + 9.84661877 Combine like terms: -9.84661877 + 9.84661877 = 0.00000000 0.00000000 + x = -10.943651993 + 9.84661877 x = -10.943651993 + 9.84661877 Combine like terms: -10.943651993 + 9.84661877 = -1.097033223 x = -1.097033223 Simplifying x = -1.097033223Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.790270763, -1.097033223}
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