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Simplifying y3 + 10y2 + -9y = 0 Reorder the terms: -9y + 10y2 + y3 = 0 Solving -9y + 10y2 + y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(-9 + 10y + 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 '(-9 + 10y + y2)' equal to zero and attempt to solve: Simplifying -9 + 10y + y2 = 0 Solving -9 + 10y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 10y + 9 + y2 = 0 + 9 Reorder the terms: -9 + 9 + 10y + y2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 10y + y2 = 0 + 9 10y + y2 = 0 + 9 Combine like terms: 0 + 9 = 9 10y + y2 = 9 The y term is 10y. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10y + 25 + y2 = 9 + 25 Reorder the terms: 25 + 10y + y2 = 9 + 25 Combine like terms: 9 + 25 = 34 25 + 10y + y2 = 34 Factor a perfect square on the left side: (y + 5)(y + 5) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (y + 5) equal to 5.830951895 and -5.830951895.Subproblem 1
y + 5 = 5.830951895 Simplifying y + 5 = 5.830951895 Reorder the terms: 5 + y = 5.830951895 Solving 5 + y = 5.830951895 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + y = 5.830951895 + -5 Combine like terms: 5 + -5 = 0 0 + y = 5.830951895 + -5 y = 5.830951895 + -5 Combine like terms: 5.830951895 + -5 = 0.830951895 y = 0.830951895 Simplifying y = 0.830951895Subproblem 2
y + 5 = -5.830951895 Simplifying y + 5 = -5.830951895 Reorder the terms: 5 + y = -5.830951895 Solving 5 + y = -5.830951895 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + y = -5.830951895 + -5 Combine like terms: 5 + -5 = 0 0 + y = -5.830951895 + -5 y = -5.830951895 + -5 Combine like terms: -5.830951895 + -5 = -10.830951895 y = -10.830951895 Simplifying y = -10.830951895Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.830951895, -10.830951895}Solution
y = {0, 0.830951895, -10.830951895}
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