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Simplifying 20y3 + -5y2 + 45y = 0 Reorder the terms: 45y + -5y2 + 20y3 = 0 Solving 45y + -5y2 + 20y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '5y'. 5y(9 + -1y + 4y2) = 0 Ignore the factor 5.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 '(9 + -1y + 4y2)' equal to zero and attempt to solve: Simplifying 9 + -1y + 4y2 = 0 Solving 9 + -1y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + -0.25y + y2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + -0.25y + -2.25 + y2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + -0.25y + y2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + -0.25y + y2 = 0 + -2.25 -0.25y + y2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 -0.25y + y2 = -2.25 The y term is -0.25y. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25y + 0.015625 + y2 = -2.25 + 0.015625 Reorder the terms: 0.015625 + -0.25y + y2 = -2.25 + 0.015625 Combine like terms: -2.25 + 0.015625 = -2.234375 0.015625 + -0.25y + y2 = -2.234375 Factor a perfect square on the left side: (y + -0.125)(y + -0.125) = -2.234375 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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