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Simplifying y3 + -5y2 + -2y = 0 Reorder the terms: -2y + -5y2 + y3 = 0 Solving -2y + -5y2 + y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(-2 + -5y + y2) = 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 '(-2 + -5y + y2)' equal to zero and attempt to solve: Simplifying -2 + -5y + y2 = 0 Solving -2 + -5y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -5y + 2 + y2 = 0 + 2 Reorder the terms: -2 + 2 + -5y + y2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5y + y2 = 0 + 2 -5y + y2 = 0 + 2 Combine like terms: 0 + 2 = 2 -5y + y2 = 2 The y term is -5y. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5y + 6.25 + y2 = 2 + 6.25 Reorder the terms: 6.25 + -5y + y2 = 2 + 6.25 Combine like terms: 2 + 6.25 = 8.25 6.25 + -5y + y2 = 8.25 Factor a perfect square on the left side: (y + -2.5)(y + -2.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (y + -2.5) equal to 2.872281323 and -2.872281323.Subproblem 1
y + -2.5 = 2.872281323 Simplifying y + -2.5 = 2.872281323 Reorder the terms: -2.5 + y = 2.872281323 Solving -2.5 + y = 2.872281323 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + y = 2.872281323 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = 2.872281323 + 2.5 y = 2.872281323 + 2.5 Combine like terms: 2.872281323 + 2.5 = 5.372281323 y = 5.372281323 Simplifying y = 5.372281323Subproblem 2
y + -2.5 = -2.872281323 Simplifying y + -2.5 = -2.872281323 Reorder the terms: -2.5 + y = -2.872281323 Solving -2.5 + y = -2.872281323 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + y = -2.872281323 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = -2.872281323 + 2.5 y = -2.872281323 + 2.5 Combine like terms: -2.872281323 + 2.5 = -0.372281323 y = -0.372281323 Simplifying y = -0.372281323Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.372281323, -0.372281323}Solution
y = {0, 5.372281323, -0.372281323}
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