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Simplifying 4y2 + -8y3 + 6y4 = 0 Solving 4y2 + -8y3 + 6y4 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2y2'. 2y2(2 + -4y + 3y2) = 0 Ignore the factor 2.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 '(2 + -4y + 3y2)' equal to zero and attempt to solve: Simplifying 2 + -4y + 3y2 = 0 Solving 2 + -4y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.6666666667 + -1.333333333y + y2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -1.333333333y + -0.6666666667 + y2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -1.333333333y + y2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -1.333333333y + y2 = 0 + -0.6666666667 -1.333333333y + y2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -1.333333333y + y2 = -0.6666666667 The y term is -1.333333333y. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333y + 0.4444444442 + y2 = -0.6666666667 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333y + y2 = -0.6666666667 + 0.4444444442 Combine like terms: -0.6666666667 + 0.4444444442 = -0.2222222225 0.4444444442 + -1.333333333y + y2 = -0.2222222225 Factor a perfect square on the left side: (y + -0.6666666665)(y + -0.6666666665) = -0.2222222225 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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