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Simplifying -10y3 + 25y2 + 30y4 = 0 Reorder the terms: 25y2 + -10y3 + 30y4 = 0 Solving 25y2 + -10y3 + 30y4 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '5y2'. 5y2(5 + -2y + 6y2) = 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 '(5 + -2y + 6y2)' equal to zero and attempt to solve: Simplifying 5 + -2y + 6y2 = 0 Solving 5 + -2y + 6y2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.8333333333 + -0.3333333333y + y2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + -0.3333333333y + -0.8333333333 + y2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + -0.3333333333y + y2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + -0.3333333333y + y2 = 0 + -0.8333333333 -0.3333333333y + y2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 -0.3333333333y + y2 = -0.8333333333 The y term is -0.3333333333y. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333y + 0.02777777779 + y2 = -0.8333333333 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333y + y2 = -0.8333333333 + 0.02777777779 Combine like terms: -0.8333333333 + 0.02777777779 = -0.80555555551 0.02777777779 + -0.3333333333y + y2 = -0.80555555551 Factor a perfect square on the left side: (y + -0.1666666667)(y + -0.1666666667) = -0.80555555551 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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