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Simplifying 6x2 + 11x = 8 Reorder the terms: 11x + 6x2 = 8 Solving 11x + 6x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + 11x + 6x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 11x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.333333333 + 1.833333333x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 1.833333333x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 1.833333333x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 1.833333333x + x2 = 0 + 1.333333333 1.833333333x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 1.833333333x + x2 = 1.333333333 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 = 1.333333333 + 0.8402777775 Reorder the terms: 0.8402777775 + 1.833333333x + x2 = 1.333333333 + 0.8402777775 Combine like terms: 1.333333333 + 0.8402777775 = 2.1736111105 0.8402777775 + 1.833333333x + x2 = 2.1736111105 Factor a perfect square on the left side: (x + 0.9166666665)(x + 0.9166666665) = 2.1736111105 Calculate the square root of the right side: 1.474317168 Break this problem into two subproblems by setting (x + 0.9166666665) equal to 1.474317168 and -1.474317168.Subproblem 1
x + 0.9166666665 = 1.474317168 Simplifying x + 0.9166666665 = 1.474317168 Reorder the terms: 0.9166666665 + x = 1.474317168 Solving 0.9166666665 + x = 1.474317168 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 = 1.474317168 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + x = 1.474317168 + -0.9166666665 x = 1.474317168 + -0.9166666665 Combine like terms: 1.474317168 + -0.9166666665 = 0.5576505015 x = 0.5576505015 Simplifying x = 0.5576505015Subproblem 2
x + 0.9166666665 = -1.474317168 Simplifying x + 0.9166666665 = -1.474317168 Reorder the terms: 0.9166666665 + x = -1.474317168 Solving 0.9166666665 + x = -1.474317168 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 = -1.474317168 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + x = -1.474317168 + -0.9166666665 x = -1.474317168 + -0.9166666665 Combine like terms: -1.474317168 + -0.9166666665 = -2.3909838345 x = -2.3909838345 Simplifying x = -2.3909838345Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5576505015, -2.3909838345}
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