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Simplifying 5y4 + 25y3 + 40y2 = 0 Reorder the terms: 40y2 + 25y3 + 5y4 = 0 Solving 40y2 + 25y3 + 5y4 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '5y2'. 5y2(8 + 5y + y2) = 0 Ignore the factor 5.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 '(8 + 5y + y2)' equal to zero and attempt to solve: Simplifying 8 + 5y + y2 = 0 Solving 8 + 5y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + 5y + -8 + y2 = 0 + -8 Reorder the terms: 8 + -8 + 5y + y2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 5y + y2 = 0 + -8 5y + y2 = 0 + -8 Combine like terms: 0 + -8 = -8 5y + y2 = -8 The y term is 5y. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5y + 6.25 + y2 = -8 + 6.25 Reorder the terms: 6.25 + 5y + y2 = -8 + 6.25 Combine like terms: -8 + 6.25 = -1.75 6.25 + 5y + y2 = -1.75 Factor a perfect square on the left side: (y + 2.5)(y + 2.5) = -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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