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Simplifying 18x2 + 44x = 11x + -30 Reorder the terms: 44x + 18x2 = 11x + -30 Reorder the terms: 44x + 18x2 = -30 + 11x Solving 44x + 18x2 = -30 + 11x Solving for variable 'x'. Reorder the terms: 30 + 44x + -11x + 18x2 = -30 + 11x + 30 + -11x Combine like terms: 44x + -11x = 33x 30 + 33x + 18x2 = -30 + 11x + 30 + -11x Reorder the terms: 30 + 33x + 18x2 = -30 + 30 + 11x + -11x Combine like terms: -30 + 30 = 0 30 + 33x + 18x2 = 0 + 11x + -11x 30 + 33x + 18x2 = 11x + -11x Combine like terms: 11x + -11x = 0 30 + 33x + 18x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(10 + 11x + 6x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(10 + 11x + 6x2)' equal to zero and attempt to solve: Simplifying 10 + 11x + 6x2 = 0 Solving 10 + 11x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.666666667 + 1.833333333x + x2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + 1.833333333x + -1.666666667 + x2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + 1.833333333x + x2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + 1.833333333x + x2 = 0 + -1.666666667 1.833333333x + x2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 1.833333333x + x2 = -1.666666667 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 = -1.666666667 + 0.8402777775 Reorder the terms: 0.8402777775 + 1.833333333x + x2 = -1.666666667 + 0.8402777775 Combine like terms: -1.666666667 + 0.8402777775 = -0.8263888895 0.8402777775 + 1.833333333x + x2 = -0.8263888895 Factor a perfect square on the left side: (x + 0.9166666665)(x + 0.9166666665) = -0.8263888895 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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