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Simplifying y3 + 3y2 + -4y + -12y = 0 Reorder the terms: -4y + -12y + 3y2 + y3 = 0 Combine like terms: -4y + -12y = -16y -16y + 3y2 + y3 = 0 Solving -16y + 3y2 + y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(-16 + 3y + 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 '(-16 + 3y + y2)' equal to zero and attempt to solve: Simplifying -16 + 3y + y2 = 0 Solving -16 + 3y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 3y + 16 + y2 = 0 + 16 Reorder the terms: -16 + 16 + 3y + y2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 3y + y2 = 0 + 16 3y + y2 = 0 + 16 Combine like terms: 0 + 16 = 16 3y + y2 = 16 The y term is 3y. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3y + 2.25 + y2 = 16 + 2.25 Reorder the terms: 2.25 + 3y + y2 = 16 + 2.25 Combine like terms: 16 + 2.25 = 18.25 2.25 + 3y + y2 = 18.25 Factor a perfect square on the left side: (y + 1.5)(y + 1.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (y + 1.5) equal to 4.272001873 and -4.272001873.Subproblem 1
y + 1.5 = 4.272001873 Simplifying y + 1.5 = 4.272001873 Reorder the terms: 1.5 + y = 4.272001873 Solving 1.5 + y = 4.272001873 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y = 4.272001873 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = 4.272001873 + -1.5 y = 4.272001873 + -1.5 Combine like terms: 4.272001873 + -1.5 = 2.772001873 y = 2.772001873 Simplifying y = 2.772001873Subproblem 2
y + 1.5 = -4.272001873 Simplifying y + 1.5 = -4.272001873 Reorder the terms: 1.5 + y = -4.272001873 Solving 1.5 + y = -4.272001873 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y = -4.272001873 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = -4.272001873 + -1.5 y = -4.272001873 + -1.5 Combine like terms: -4.272001873 + -1.5 = -5.772001873 y = -5.772001873 Simplifying y = -5.772001873Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.772001873, -5.772001873}Solution
y = {0, 2.772001873, -5.772001873}
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