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Simplifying 12x2 + -22x + 68 = 0 Reorder the terms: 68 + -22x + 12x2 = 0 Solving 68 + -22x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(34 + -11x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(34 + -11x + 6x2)' equal to zero and attempt to solve: Simplifying 34 + -11x + 6x2 = 0 Solving 34 + -11x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 5.666666667 + -1.833333333x + x2 = 0 Move the constant term to the right: Add '-5.666666667' to each side of the equation. 5.666666667 + -1.833333333x + -5.666666667 + x2 = 0 + -5.666666667 Reorder the terms: 5.666666667 + -5.666666667 + -1.833333333x + x2 = 0 + -5.666666667 Combine like terms: 5.666666667 + -5.666666667 = 0.000000000 0.000000000 + -1.833333333x + x2 = 0 + -5.666666667 -1.833333333x + x2 = 0 + -5.666666667 Combine like terms: 0 + -5.666666667 = -5.666666667 -1.833333333x + x2 = -5.666666667 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 = -5.666666667 + 0.8402777775 Reorder the terms: 0.8402777775 + -1.833333333x + x2 = -5.666666667 + 0.8402777775 Combine like terms: -5.666666667 + 0.8402777775 = -4.8263888895 0.8402777775 + -1.833333333x + x2 = -4.8263888895 Factor a perfect square on the left side: (x + -0.9166666665)(x + -0.9166666665) = -4.8263888895 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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