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Simplifying 9y3 + -18y2 + 45y = 0 Reorder the terms: 45y + -18y2 + 9y3 = 0 Solving 45y + -18y2 + 9y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '9y'. 9y(5 + -2y + y2) = 0 Ignore the factor 9.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 '(5 + -2y + y2)' equal to zero and attempt to solve: Simplifying 5 + -2y + y2 = 0 Solving 5 + -2y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -2y + -5 + y2 = 0 + -5 Reorder the terms: 5 + -5 + -2y + y2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2y + y2 = 0 + -5 -2y + y2 = 0 + -5 Combine like terms: 0 + -5 = -5 -2y + y2 = -5 The y term is -2y. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2y + 1 + y2 = -5 + 1 Reorder the terms: 1 + -2y + y2 = -5 + 1 Combine like terms: -5 + 1 = -4 1 + -2y + y2 = -4 Factor a perfect square on the left side: (y + -1)(y + -1) = -4 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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