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Simplifying 15y5 + -25y4 + 35y3 = 0 Reorder the terms: 35y3 + -25y4 + 15y5 = 0 Solving 35y3 + -25y4 + 15y5 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '5y3'. 5y3(7 + -5y + 3y2) = 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 '(7 + -5y + 3y2)' equal to zero and attempt to solve: Simplifying 7 + -5y + 3y2 = 0 Solving 7 + -5y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.333333333 + -1.666666667y + y2 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + -1.666666667y + -2.333333333 + y2 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + -1.666666667y + y2 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + -1.666666667y + y2 = 0 + -2.333333333 -1.666666667y + y2 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 -1.666666667y + y2 = -2.333333333 The y term is -1.666666667y. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667y + 0.6944444447 + y2 = -2.333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667y + y2 = -2.333333333 + 0.6944444447 Combine like terms: -2.333333333 + 0.6944444447 = -1.6388888883 0.6944444447 + -1.666666667y + y2 = -1.6388888883 Factor a perfect square on the left side: (y + -0.8333333335)(y + -0.8333333335) = -1.6388888883 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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