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Simplifying 9y2 + 6y + 12 = 0 Reorder the terms: 12 + 6y + 9y2 = 0 Solving 12 + 6y + 9y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3'. 3(4 + 2y + 3y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + 2y + 3y2)' equal to zero and attempt to solve: Simplifying 4 + 2y + 3y2 = 0 Solving 4 + 2y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + 0.6666666667y + y2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + 0.6666666667y + -1.333333333 + y2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + 0.6666666667y + y2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + 0.6666666667y + y2 = 0 + -1.333333333 0.6666666667y + y2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 0.6666666667y + y2 = -1.333333333 The y term is 0.6666666667y. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667y + 0.1111111112 + y2 = -1.333333333 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667y + y2 = -1.333333333 + 0.1111111112 Combine like terms: -1.333333333 + 0.1111111112 = -1.2222222218 0.1111111112 + 0.6666666667y + y2 = -1.2222222218 Factor a perfect square on the left side: (y + 0.3333333334)(y + 0.3333333334) = -1.2222222218 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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