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Simplifying 2y3 + 2y2 + 10y = 0 Reorder the terms: 10y + 2y2 + 2y3 = 0 Solving 10y + 2y2 + 2y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2y'. 2y(5 + y + y2) = 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 '(5 + y + y2)' equal to zero and attempt to solve: Simplifying 5 + y + y2 = 0 Solving 5 + y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + y + -5 + y2 = 0 + -5 Reorder the terms: 5 + -5 + y + y2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + y + y2 = 0 + -5 y + y2 = 0 + -5 Combine like terms: 0 + -5 = -5 y + y2 = -5 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 = -5 + 0.25 Reorder the terms: 0.25 + y + y2 = -5 + 0.25 Combine like terms: -5 + 0.25 = -4.75 0.25 + y + y2 = -4.75 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = -4.75 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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