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Simplifying 6y2 + 9y = 11y + -4 Reorder the terms: 9y + 6y2 = 11y + -4 Reorder the terms: 9y + 6y2 = -4 + 11y Solving 9y + 6y2 = -4 + 11y Solving for variable 'y'. Reorder the terms: 4 + 9y + -11y + 6y2 = -4 + 11y + 4 + -11y Combine like terms: 9y + -11y = -2y 4 + -2y + 6y2 = -4 + 11y + 4 + -11y Reorder the terms: 4 + -2y + 6y2 = -4 + 4 + 11y + -11y Combine like terms: -4 + 4 = 0 4 + -2y + 6y2 = 0 + 11y + -11y 4 + -2y + 6y2 = 11y + -11y Combine like terms: 11y + -11y = 0 4 + -2y + 6y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -1y + 3y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -1y + 3y2)' equal to zero and attempt to solve: Simplifying 2 + -1y + 3y2 = 0 Solving 2 + -1y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.6666666667 + -0.3333333333y + y2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -0.3333333333y + -0.6666666667 + y2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -0.3333333333y + y2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -0.3333333333y + y2 = 0 + -0.6666666667 -0.3333333333y + y2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -0.3333333333y + y2 = -0.6666666667 The y term is -0.3333333333y. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333y + 0.02777777779 + y2 = -0.6666666667 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333y + y2 = -0.6666666667 + 0.02777777779 Combine like terms: -0.6666666667 + 0.02777777779 = -0.63888888891 0.02777777779 + -0.3333333333y + y2 = -0.63888888891 Factor a perfect square on the left side: (y + -0.1666666667)(y + -0.1666666667) = -0.63888888891 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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