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Simplifying 12x2 + -11x + -40 = 0 Reorder the terms: -40 + -11x + 12x2 = 0 Solving -40 + -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'. -3.333333333 + -0.9166666667x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + -0.9166666667x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + -0.9166666667x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + -0.9166666667x + x2 = 0 + 3.333333333 -0.9166666667x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 -0.9166666667x + x2 = 3.333333333 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 = 3.333333333 + 0.2100694445 Reorder the terms: 0.2100694445 + -0.9166666667x + x2 = 3.333333333 + 0.2100694445 Combine like terms: 3.333333333 + 0.2100694445 = 3.5434027775 0.2100694445 + -0.9166666667x + x2 = 3.5434027775 Factor a perfect square on the left side: (x + -0.4583333334)(x + -0.4583333334) = 3.5434027775 Calculate the square root of the right side: 1.882392833 Break this problem into two subproblems by setting (x + -0.4583333334) equal to 1.882392833 and -1.882392833.Subproblem 1
x + -0.4583333334 = 1.882392833 Simplifying x + -0.4583333334 = 1.882392833 Reorder the terms: -0.4583333334 + x = 1.882392833 Solving -0.4583333334 + x = 1.882392833 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 = 1.882392833 + 0.4583333334 Combine like terms: -0.4583333334 + 0.4583333334 = 0.0000000000 0.0000000000 + x = 1.882392833 + 0.4583333334 x = 1.882392833 + 0.4583333334 Combine like terms: 1.882392833 + 0.4583333334 = 2.3407261664 x = 2.3407261664 Simplifying x = 2.3407261664Subproblem 2
x + -0.4583333334 = -1.882392833 Simplifying x + -0.4583333334 = -1.882392833 Reorder the terms: -0.4583333334 + x = -1.882392833 Solving -0.4583333334 + x = -1.882392833 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 = -1.882392833 + 0.4583333334 Combine like terms: -0.4583333334 + 0.4583333334 = 0.0000000000 0.0000000000 + x = -1.882392833 + 0.4583333334 x = -1.882392833 + 0.4583333334 Combine like terms: -1.882392833 + 0.4583333334 = -1.4240594996 x = -1.4240594996 Simplifying x = -1.4240594996Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3407261664, -1.4240594996}
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