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Simplifying y3 + y2 + 3y + y = 0 Reorder the terms: 3y + y + y2 + y3 = 0 Combine like terms: 3y + y = 4y 4y + y2 + y3 = 0 Solving 4y + y2 + y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(4 + y + y2) = 0Subproblem 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 '(4 + y + y2)' equal to zero and attempt to solve: Simplifying 4 + y + y2 = 0 Solving 4 + y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + y + -4 + y2 = 0 + -4 Reorder the terms: 4 + -4 + y + y2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + y + y2 = 0 + -4 y + y2 = 0 + -4 Combine like terms: 0 + -4 = -4 y + y2 = -4 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 = -4 + 0.25 Reorder the terms: 0.25 + y + y2 = -4 + 0.25 Combine like terms: -4 + 0.25 = -3.75 0.25 + y + y2 = -3.75 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = -3.75 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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