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Simplifying 11x2 + -4x + -6 = 0 Reorder the terms: -6 + -4x + 11x2 = 0 Solving -6 + -4x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.5454545455 + -0.3636363636x + x2 = 0 Move the constant term to the right: Add '0.5454545455' to each side of the equation. -0.5454545455 + -0.3636363636x + 0.5454545455 + x2 = 0 + 0.5454545455 Reorder the terms: -0.5454545455 + 0.5454545455 + -0.3636363636x + x2 = 0 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + -0.3636363636x + x2 = 0 + 0.5454545455 -0.3636363636x + x2 = 0 + 0.5454545455 Combine like terms: 0 + 0.5454545455 = 0.5454545455 -0.3636363636x + x2 = 0.5454545455 The x term is -0.3636363636x. Take half its coefficient (-0.1818181818). Square it (0.03305785123) and add it to both sides. Add '0.03305785123' to each side of the equation. -0.3636363636x + 0.03305785123 + x2 = 0.5454545455 + 0.03305785123 Reorder the terms: 0.03305785123 + -0.3636363636x + x2 = 0.5454545455 + 0.03305785123 Combine like terms: 0.5454545455 + 0.03305785123 = 0.57851239673 0.03305785123 + -0.3636363636x + x2 = 0.57851239673 Factor a perfect square on the left side: (x + -0.1818181818)(x + -0.1818181818) = 0.57851239673 Calculate the square root of the right side: 0.760600024 Break this problem into two subproblems by setting (x + -0.1818181818) equal to 0.760600024 and -0.760600024.Subproblem 1
x + -0.1818181818 = 0.760600024 Simplifying x + -0.1818181818 = 0.760600024 Reorder the terms: -0.1818181818 + x = 0.760600024 Solving -0.1818181818 + x = 0.760600024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1818181818' to each side of the equation. -0.1818181818 + 0.1818181818 + x = 0.760600024 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + x = 0.760600024 + 0.1818181818 x = 0.760600024 + 0.1818181818 Combine like terms: 0.760600024 + 0.1818181818 = 0.9424182058 x = 0.9424182058 Simplifying x = 0.9424182058Subproblem 2
x + -0.1818181818 = -0.760600024 Simplifying x + -0.1818181818 = -0.760600024 Reorder the terms: -0.1818181818 + x = -0.760600024 Solving -0.1818181818 + x = -0.760600024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1818181818' to each side of the equation. -0.1818181818 + 0.1818181818 + x = -0.760600024 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + x = -0.760600024 + 0.1818181818 x = -0.760600024 + 0.1818181818 Combine like terms: -0.760600024 + 0.1818181818 = -0.5787818422 x = -0.5787818422 Simplifying x = -0.5787818422Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9424182058, -0.5787818422}
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