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Simplifying 0 = 6x2 + -11x + -4 Reorder the terms: 0 = -4 + -11x + 6x2 Solving 0 = -4 + -11x + 6x2 Solving for variable 'x'. Combine like terms: 0 + 4 = 4 4 + 11x + -6x2 = -4 + -11x + 6x2 + 4 + 11x + -6x2 Reorder the terms: 4 + 11x + -6x2 = -4 + 4 + -11x + 11x + 6x2 + -6x2 Combine like terms: -4 + 4 = 0 4 + 11x + -6x2 = 0 + -11x + 11x + 6x2 + -6x2 4 + 11x + -6x2 = -11x + 11x + 6x2 + -6x2 Combine like terms: -11x + 11x = 0 4 + 11x + -6x2 = 0 + 6x2 + -6x2 4 + 11x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 4 + 11x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -0.6666666667 + -1.833333333x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -1.833333333x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -1.833333333x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -1.833333333x + x2 = 0 + 0.6666666667 -1.833333333x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -1.833333333x + x2 = 0.6666666667 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 = 0.6666666667 + 0.8402777775 Reorder the terms: 0.8402777775 + -1.833333333x + x2 = 0.6666666667 + 0.8402777775 Combine like terms: 0.6666666667 + 0.8402777775 = 1.5069444442 0.8402777775 + -1.833333333x + x2 = 1.5069444442 Factor a perfect square on the left side: (x + -0.9166666665)(x + -0.9166666665) = 1.5069444442 Calculate the square root of the right side: 1.227576655 Break this problem into two subproblems by setting (x + -0.9166666665) equal to 1.227576655 and -1.227576655.Subproblem 1
x + -0.9166666665 = 1.227576655 Simplifying x + -0.9166666665 = 1.227576655 Reorder the terms: -0.9166666665 + x = 1.227576655 Solving -0.9166666665 + x = 1.227576655 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 = 1.227576655 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = 1.227576655 + 0.9166666665 x = 1.227576655 + 0.9166666665 Combine like terms: 1.227576655 + 0.9166666665 = 2.1442433215 x = 2.1442433215 Simplifying x = 2.1442433215Subproblem 2
x + -0.9166666665 = -1.227576655 Simplifying x + -0.9166666665 = -1.227576655 Reorder the terms: -0.9166666665 + x = -1.227576655 Solving -0.9166666665 + x = -1.227576655 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 = -1.227576655 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = -1.227576655 + 0.9166666665 x = -1.227576655 + 0.9166666665 Combine like terms: -1.227576655 + 0.9166666665 = -0.3109099885 x = -0.3109099885 Simplifying x = -0.3109099885Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1442433215, -0.3109099885}
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