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Simplifying y4 + 7y3 + 18y2 = 0 Reorder the terms: 18y2 + 7y3 + y4 = 0 Solving 18y2 + 7y3 + y4 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y2'. y2(18 + 7y + y2) = 0Subproblem 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 '(18 + 7y + y2)' equal to zero and attempt to solve: Simplifying 18 + 7y + y2 = 0 Solving 18 + 7y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + 7y + -18 + y2 = 0 + -18 Reorder the terms: 18 + -18 + 7y + y2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + 7y + y2 = 0 + -18 7y + y2 = 0 + -18 Combine like terms: 0 + -18 = -18 7y + y2 = -18 The y term is 7y. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7y + 12.25 + y2 = -18 + 12.25 Reorder the terms: 12.25 + 7y + y2 = -18 + 12.25 Combine like terms: -18 + 12.25 = -5.75 12.25 + 7y + y2 = -5.75 Factor a perfect square on the left side: (y + 3.5)(y + 3.5) = -5.75 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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