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Simplifying y4 + 15y3 + 60y2 = 0 Reorder the terms: 60y2 + 15y3 + y4 = 0 Solving 60y2 + 15y3 + y4 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y2'. y2(60 + 15y + y2) = 0Subproblem 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 '(60 + 15y + y2)' equal to zero and attempt to solve: Simplifying 60 + 15y + y2 = 0 Solving 60 + 15y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-60' to each side of the equation. 60 + 15y + -60 + y2 = 0 + -60 Reorder the terms: 60 + -60 + 15y + y2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + 15y + y2 = 0 + -60 15y + y2 = 0 + -60 Combine like terms: 0 + -60 = -60 15y + y2 = -60 The y term is 15y. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15y + 56.25 + y2 = -60 + 56.25 Reorder the terms: 56.25 + 15y + y2 = -60 + 56.25 Combine like terms: -60 + 56.25 = -3.75 56.25 + 15y + y2 = -3.75 Factor a perfect square on the left side: (y + 7.5)(y + 7.5) = -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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