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Simplifying y + 3y + -5y2 + 7y3 + -4y2 = 0 Reorder the terms: y + 3y + -5y2 + -4y2 + 7y3 = 0 Combine like terms: y + 3y = 4y 4y + -5y2 + -4y2 + 7y3 = 0 Combine like terms: -5y2 + -4y2 = -9y2 4y + -9y2 + 7y3 = 0 Solving 4y + -9y2 + 7y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(4 + -9y + 7y2) = 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 + -9y + 7y2)' equal to zero and attempt to solve: Simplifying 4 + -9y + 7y2 = 0 Solving 4 + -9y + 7y2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.5714285714 + -1.285714286y + y2 = 0 Move the constant term to the right: Add '-0.5714285714' to each side of the equation. 0.5714285714 + -1.285714286y + -0.5714285714 + y2 = 0 + -0.5714285714 Reorder the terms: 0.5714285714 + -0.5714285714 + -1.285714286y + y2 = 0 + -0.5714285714 Combine like terms: 0.5714285714 + -0.5714285714 = 0.0000000000 0.0000000000 + -1.285714286y + y2 = 0 + -0.5714285714 -1.285714286y + y2 = 0 + -0.5714285714 Combine like terms: 0 + -0.5714285714 = -0.5714285714 -1.285714286y + y2 = -0.5714285714 The y term is -1.285714286y. Take half its coefficient (-0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. -1.285714286y + 0.4132653063 + y2 = -0.5714285714 + 0.4132653063 Reorder the terms: 0.4132653063 + -1.285714286y + y2 = -0.5714285714 + 0.4132653063 Combine like terms: -0.5714285714 + 0.4132653063 = -0.1581632651 0.4132653063 + -1.285714286y + y2 = -0.1581632651 Factor a perfect square on the left side: (y + -0.642857143)(y + -0.642857143) = -0.1581632651 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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