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Simplifying 12x2 + -5x + -24 = 0 Reorder the terms: -24 + -5x + 12x2 = 0 Solving -24 + -5x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -2 + -0.4166666667x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.4166666667x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -0.4166666667x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.4166666667x + x2 = 0 + 2 -0.4166666667x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.4166666667x + x2 = 2 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 = 2 + 0.04340277781 Reorder the terms: 0.04340277781 + -0.4166666667x + x2 = 2 + 0.04340277781 Combine like terms: 2 + 0.04340277781 = 2.04340277781 0.04340277781 + -0.4166666667x + x2 = 2.04340277781 Factor a perfect square on the left side: (x + -0.2083333334)(x + -0.2083333334) = 2.04340277781 Calculate the square root of the right side: 1.4294764 Break this problem into two subproblems by setting (x + -0.2083333334) equal to 1.4294764 and -1.4294764.Subproblem 1
x + -0.2083333334 = 1.4294764 Simplifying x + -0.2083333334 = 1.4294764 Reorder the terms: -0.2083333334 + x = 1.4294764 Solving -0.2083333334 + x = 1.4294764 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 = 1.4294764 + 0.2083333334 Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000 0.0000000000 + x = 1.4294764 + 0.2083333334 x = 1.4294764 + 0.2083333334 Combine like terms: 1.4294764 + 0.2083333334 = 1.6378097334 x = 1.6378097334 Simplifying x = 1.6378097334Subproblem 2
x + -0.2083333334 = -1.4294764 Simplifying x + -0.2083333334 = -1.4294764 Reorder the terms: -0.2083333334 + x = -1.4294764 Solving -0.2083333334 + x = -1.4294764 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 = -1.4294764 + 0.2083333334 Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000 0.0000000000 + x = -1.4294764 + 0.2083333334 x = -1.4294764 + 0.2083333334 Combine like terms: -1.4294764 + 0.2083333334 = -1.2211430666 x = -1.2211430666 Simplifying x = -1.2211430666Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6378097334, -1.2211430666}
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