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Simplifying 12x2 + -11x + -24 = 0 Reorder the terms: -24 + -11x + 12x2 = 0 Solving -24 + -11x + 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 + -0.9166666667x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.9166666667x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -0.9166666667x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.9166666667x + x2 = 0 + 2 -0.9166666667x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.9166666667x + x2 = 2 The x term is -0.9166666667x. Take half its coefficient (-0.4583333334). Square it (0.2100694445) and add it to both sides. Add '0.2100694445' to each side of the equation. -0.9166666667x + 0.2100694445 + x2 = 2 + 0.2100694445 Reorder the terms: 0.2100694445 + -0.9166666667x + x2 = 2 + 0.2100694445 Combine like terms: 2 + 0.2100694445 = 2.2100694445 0.2100694445 + -0.9166666667x + x2 = 2.2100694445 Factor a perfect square on the left side: (x + -0.4583333334)(x + -0.4583333334) = 2.2100694445 Calculate the square root of the right side: 1.486630231 Break this problem into two subproblems by setting (x + -0.4583333334) equal to 1.486630231 and -1.486630231.Subproblem 1
x + -0.4583333334 = 1.486630231 Simplifying x + -0.4583333334 = 1.486630231 Reorder the terms: -0.4583333334 + x = 1.486630231 Solving -0.4583333334 + x = 1.486630231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4583333334' to each side of the equation. -0.4583333334 + 0.4583333334 + x = 1.486630231 + 0.4583333334 Combine like terms: -0.4583333334 + 0.4583333334 = 0.0000000000 0.0000000000 + x = 1.486630231 + 0.4583333334 x = 1.486630231 + 0.4583333334 Combine like terms: 1.486630231 + 0.4583333334 = 1.9449635644 x = 1.9449635644 Simplifying x = 1.9449635644Subproblem 2
x + -0.4583333334 = -1.486630231 Simplifying x + -0.4583333334 = -1.486630231 Reorder the terms: -0.4583333334 + x = -1.486630231 Solving -0.4583333334 + x = -1.486630231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4583333334' to each side of the equation. -0.4583333334 + 0.4583333334 + x = -1.486630231 + 0.4583333334 Combine like terms: -0.4583333334 + 0.4583333334 = 0.0000000000 0.0000000000 + x = -1.486630231 + 0.4583333334 x = -1.486630231 + 0.4583333334 Combine like terms: -1.486630231 + 0.4583333334 = -1.0282968976 x = -1.0282968976 Simplifying x = -1.0282968976Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9449635644, -1.0282968976}
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