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Simplifying 0 = 24 + -22x + 12x2 Solving 0 = 24 + -22x + 12x2 Solving for variable 'x'. Combine like terms: 0 + -24 = -24 -24 + 22x + -12x2 = 24 + -22x + 12x2 + -24 + 22x + -12x2 Reorder the terms: -24 + 22x + -12x2 = 24 + -24 + -22x + 22x + 12x2 + -12x2 Combine like terms: 24 + -24 = 0 -24 + 22x + -12x2 = 0 + -22x + 22x + 12x2 + -12x2 -24 + 22x + -12x2 = -22x + 22x + 12x2 + -12x2 Combine like terms: -22x + 22x = 0 -24 + 22x + -12x2 = 0 + 12x2 + -12x2 -24 + 22x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -24 + 22x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + 11x + -6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + 11x + -6x2)' equal to zero and attempt to solve: Simplifying -12 + 11x + -6x2 = 0 Solving -12 + 11x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 2 + -1.833333333x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -1.833333333x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -1.833333333x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1.833333333x + x2 = 0 + -2 -1.833333333x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1.833333333x + x2 = -2 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 = -2 + 0.8402777775 Reorder the terms: 0.8402777775 + -1.833333333x + x2 = -2 + 0.8402777775 Combine like terms: -2 + 0.8402777775 = -1.1597222225 0.8402777775 + -1.833333333x + x2 = -1.1597222225 Factor a perfect square on the left side: (x + -0.9166666665)(x + -0.9166666665) = -1.1597222225 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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