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Simplifying 3y5 + 20y4 + 75y3 = 0 Reorder the terms: 75y3 + 20y4 + 3y5 = 0 Solving 75y3 + 20y4 + 3y5 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y3'. y3(75 + 20y + 3y2) = 0Subproblem 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 '(75 + 20y + 3y2)' equal to zero and attempt to solve: Simplifying 75 + 20y + 3y2 = 0 Solving 75 + 20y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 25 + 6.666666667y + y2 = 0 Move the constant term to the right: Add '-25' to each side of the equation. 25 + 6.666666667y + -25 + y2 = 0 + -25 Reorder the terms: 25 + -25 + 6.666666667y + y2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 6.666666667y + y2 = 0 + -25 6.666666667y + y2 = 0 + -25 Combine like terms: 0 + -25 = -25 6.666666667y + y2 = -25 The y term is 6.666666667y. Take half its coefficient (3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. 6.666666667y + 11.11111112 + y2 = -25 + 11.11111112 Reorder the terms: 11.11111112 + 6.666666667y + y2 = -25 + 11.11111112 Combine like terms: -25 + 11.11111112 = -13.88888888 11.11111112 + 6.666666667y + y2 = -13.88888888 Factor a perfect square on the left side: (y + 3.333333334)(y + 3.333333334) = -13.88888888 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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