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Simplifying 6x2 + -17x + -1 = -6x + -2 Reorder the terms: -1 + -17x + 6x2 = -6x + -2 Reorder the terms: -1 + -17x + 6x2 = -2 + -6x Solving -1 + -17x + 6x2 = -2 + -6x Solving for variable 'x'. Reorder the terms: -1 + 2 + -17x + 6x + 6x2 = -2 + -6x + 2 + 6x Combine like terms: -1 + 2 = 1 1 + -17x + 6x + 6x2 = -2 + -6x + 2 + 6x Combine like terms: -17x + 6x = -11x 1 + -11x + 6x2 = -2 + -6x + 2 + 6x Reorder the terms: 1 + -11x + 6x2 = -2 + 2 + -6x + 6x Combine like terms: -2 + 2 = 0 1 + -11x + 6x2 = 0 + -6x + 6x 1 + -11x + 6x2 = -6x + 6x Combine like terms: -6x + 6x = 0 1 + -11x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.1666666667 + -1.833333333x + x2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + -1.833333333x + -0.1666666667 + x2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + -1.833333333x + x2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + -1.833333333x + x2 = 0 + -0.1666666667 -1.833333333x + x2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 -1.833333333x + x2 = -0.1666666667 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 = -0.1666666667 + 0.8402777775 Reorder the terms: 0.8402777775 + -1.833333333x + x2 = -0.1666666667 + 0.8402777775 Combine like terms: -0.1666666667 + 0.8402777775 = 0.6736111108 0.8402777775 + -1.833333333x + x2 = 0.6736111108 Factor a perfect square on the left side: (x + -0.9166666665)(x + -0.9166666665) = 0.6736111108 Calculate the square root of the right side: 0.82073815 Break this problem into two subproblems by setting (x + -0.9166666665) equal to 0.82073815 and -0.82073815.Subproblem 1
x + -0.9166666665 = 0.82073815 Simplifying x + -0.9166666665 = 0.82073815 Reorder the terms: -0.9166666665 + x = 0.82073815 Solving -0.9166666665 + x = 0.82073815 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 = 0.82073815 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = 0.82073815 + 0.9166666665 x = 0.82073815 + 0.9166666665 Combine like terms: 0.82073815 + 0.9166666665 = 1.7374048165 x = 1.7374048165 Simplifying x = 1.7374048165Subproblem 2
x + -0.9166666665 = -0.82073815 Simplifying x + -0.9166666665 = -0.82073815 Reorder the terms: -0.9166666665 + x = -0.82073815 Solving -0.9166666665 + x = -0.82073815 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 = -0.82073815 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = -0.82073815 + 0.9166666665 x = -0.82073815 + 0.9166666665 Combine like terms: -0.82073815 + 0.9166666665 = 0.0959285165 x = 0.0959285165 Simplifying x = 0.0959285165Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7374048165, 0.0959285165}
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