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Simplifying 5y5 + 25y4 + 45y3 = 0 Reorder the terms: 45y3 + 25y4 + 5y5 = 0 Solving 45y3 + 25y4 + 5y5 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '5y3'. 5y3(9 + 5y + y2) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'y3' equal to zero and attempt to solve: Simplifying y3 = 0 Solving y3 = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(9 + 5y + y2)' equal to zero and attempt to solve: Simplifying 9 + 5y + y2 = 0 Solving 9 + 5y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 5y + -9 + y2 = 0 + -9 Reorder the terms: 9 + -9 + 5y + y2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 5y + y2 = 0 + -9 5y + y2 = 0 + -9 Combine like terms: 0 + -9 = -9 5y + y2 = -9 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 = -9 + 6.25 Reorder the terms: 6.25 + 5y + y2 = -9 + 6.25 Combine like terms: -9 + 6.25 = -2.75 6.25 + 5y + y2 = -2.75 Factor a perfect square on the left side: (y + 2.5)(y + 2.5) = -2.75 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. The solution to this equation could not be determined.
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