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Simplifying 3y3 + 4y2 + 4y = 0 Reorder the terms: 4y + 4y2 + 3y3 = 0 Solving 4y + 4y2 + 3y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(4 + 4y + 3y2) = 0Subproblem 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 '(4 + 4y + 3y2)' equal to zero and attempt to solve: Simplifying 4 + 4y + 3y2 = 0 Solving 4 + 4y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + 1.333333333y + y2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + 1.333333333y + -1.333333333 + y2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + 1.333333333y + y2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + 1.333333333y + y2 = 0 + -1.333333333 1.333333333y + y2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 1.333333333y + y2 = -1.333333333 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 = -1.333333333 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333y + y2 = -1.333333333 + 0.4444444442 Combine like terms: -1.333333333 + 0.4444444442 = -0.8888888888 0.4444444442 + 1.333333333y + y2 = -0.8888888888 Factor a perfect square on the left side: (y + 0.6666666665)(y + 0.6666666665) = -0.8888888888 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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