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Simplifying 9y4 + 9y3 + 18y2 = 0 Reorder the terms: 18y2 + 9y3 + 9y4 = 0 Solving 18y2 + 9y3 + 9y4 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '9y2'. 9y2(2 + y + y2) = 0 Ignore the factor 9.Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve: Simplifying y2 = 0 Solving y2 = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y2 = 0 Take the square root of each side: y = {0}Subproblem 2
Set the factor '(2 + y + y2)' equal to zero and attempt to solve: Simplifying 2 + y + y2 = 0 Solving 2 + y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + y + -2 + y2 = 0 + -2 Reorder the terms: 2 + -2 + y + y2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + y + y2 = 0 + -2 y + y2 = 0 + -2 Combine like terms: 0 + -2 = -2 y + y2 = -2 The y term is y. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. y + 0.25 + y2 = -2 + 0.25 Reorder the terms: 0.25 + y + y2 = -2 + 0.25 Combine like terms: -2 + 0.25 = -1.75 0.25 + y + y2 = -1.75 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = -1.75 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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