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Simplifying 6x2 + -11x + -20 = 0 Reorder the terms: -20 + -11x + 6x2 = 0 Solving -20 + -11x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -3.333333333 + -1.833333333x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + -1.833333333x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + -1.833333333x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + -1.833333333x + x2 = 0 + 3.333333333 -1.833333333x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 -1.833333333x + x2 = 3.333333333 The x term is -1.833333333x. Take half its coefficient (-0.9166666665). Square it (0.8402777775) and add it to both sides. Add '0.8402777775' to each side of the equation. -1.833333333x + 0.8402777775 + x2 = 3.333333333 + 0.8402777775 Reorder the terms: 0.8402777775 + -1.833333333x + x2 = 3.333333333 + 0.8402777775 Combine like terms: 3.333333333 + 0.8402777775 = 4.1736111105 0.8402777775 + -1.833333333x + x2 = 4.1736111105 Factor a perfect square on the left side: (x + -0.9166666665)(x + -0.9166666665) = 4.1736111105 Calculate the square root of the right side: 2.042941779 Break this problem into two subproblems by setting (x + -0.9166666665) equal to 2.042941779 and -2.042941779.Subproblem 1
x + -0.9166666665 = 2.042941779 Simplifying x + -0.9166666665 = 2.042941779 Reorder the terms: -0.9166666665 + x = 2.042941779 Solving -0.9166666665 + x = 2.042941779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + x = 2.042941779 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = 2.042941779 + 0.9166666665 x = 2.042941779 + 0.9166666665 Combine like terms: 2.042941779 + 0.9166666665 = 2.9596084455 x = 2.9596084455 Simplifying x = 2.9596084455Subproblem 2
x + -0.9166666665 = -2.042941779 Simplifying x + -0.9166666665 = -2.042941779 Reorder the terms: -0.9166666665 + x = -2.042941779 Solving -0.9166666665 + x = -2.042941779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + x = -2.042941779 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = -2.042941779 + 0.9166666665 x = -2.042941779 + 0.9166666665 Combine like terms: -2.042941779 + 0.9166666665 = -1.1262751125 x = -1.1262751125 Simplifying x = -1.1262751125Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.9596084455, -1.1262751125}
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