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Simplifying 8y3 + -4y2 + 10y = 0 Reorder the terms: 10y + -4y2 + 8y3 = 0 Solving 10y + -4y2 + 8y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2y'. 2y(5 + -2y + 4y2) = 0 Ignore the factor 2.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 '(5 + -2y + 4y2)' equal to zero and attempt to solve: Simplifying 5 + -2y + 4y2 = 0 Solving 5 + -2y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + -0.5y + y2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -0.5y + -1.25 + y2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -0.5y + y2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -0.5y + y2 = 0 + -1.25 -0.5y + y2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -0.5y + y2 = -1.25 The y term is -0.5y. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5y + 0.0625 + y2 = -1.25 + 0.0625 Reorder the terms: 0.0625 + -0.5y + y2 = -1.25 + 0.0625 Combine like terms: -1.25 + 0.0625 = -1.1875 0.0625 + -0.5y + y2 = -1.1875 Factor a perfect square on the left side: (y + -0.25)(y + -0.25) = -1.1875 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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