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Simplifying 18y3 + 6y2 + 2y = 0 Reorder the terms: 2y + 6y2 + 18y3 = 0 Solving 2y + 6y2 + 18y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2y'. 2y(1 + 3y + 9y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y = 0Subproblem 2
Set the factor '(1 + 3y + 9y2)' equal to zero and attempt to solve: Simplifying 1 + 3y + 9y2 = 0 Solving 1 + 3y + 9y2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.1111111111 + 0.3333333333y + y2 = 0 Move the constant term to the right: Add '-0.1111111111' to each side of the equation. 0.1111111111 + 0.3333333333y + -0.1111111111 + y2 = 0 + -0.1111111111 Reorder the terms: 0.1111111111 + -0.1111111111 + 0.3333333333y + y2 = 0 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + 0.3333333333y + y2 = 0 + -0.1111111111 0.3333333333y + y2 = 0 + -0.1111111111 Combine like terms: 0 + -0.1111111111 = -0.1111111111 0.3333333333y + y2 = -0.1111111111 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 = -0.1111111111 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333y + y2 = -0.1111111111 + 0.02777777779 Combine like terms: -0.1111111111 + 0.02777777779 = -0.08333333331 0.02777777779 + 0.3333333333y + y2 = -0.08333333331 Factor a perfect square on the left side: (y + 0.1666666667)(y + 0.1666666667) = -0.08333333331 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.Solution
y = {0}
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