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Simplifying -6x2 + -11x + -9 = 0 Reorder the terms: -9 + -11x + -6x2 = 0 Solving -9 + -11x + -6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 11x + 6x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + 11x + 6x2)' equal to zero and attempt to solve: Simplifying 9 + 11x + 6x2 = 0 Solving 9 + 11x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.5 + 1.833333333x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 1.833333333x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 1.833333333x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 1.833333333x + x2 = 0 + -1.5 1.833333333x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 1.833333333x + x2 = -1.5 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 = -1.5 + 0.8402777775 Reorder the terms: 0.8402777775 + 1.833333333x + x2 = -1.5 + 0.8402777775 Combine like terms: -1.5 + 0.8402777775 = -0.6597222225 0.8402777775 + 1.833333333x + x2 = -0.6597222225 Factor a perfect square on the left side: (x + 0.9166666665)(x + 0.9166666665) = -0.6597222225 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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