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Simplifying 2y3 + 22y2 + 24y = 0 Reorder the terms: 24y + 22y2 + 2y3 = 0 Solving 24y + 22y2 + 2y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2y'. 2y(12 + 11y + y2) = 0 Ignore the factor 2.Subproblem 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 '(12 + 11y + y2)' equal to zero and attempt to solve: Simplifying 12 + 11y + y2 = 0 Solving 12 + 11y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 11y + -12 + y2 = 0 + -12 Reorder the terms: 12 + -12 + 11y + y2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 11y + y2 = 0 + -12 11y + y2 = 0 + -12 Combine like terms: 0 + -12 = -12 11y + y2 = -12 The y term is 11y. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11y + 30.25 + y2 = -12 + 30.25 Reorder the terms: 30.25 + 11y + y2 = -12 + 30.25 Combine like terms: -12 + 30.25 = 18.25 30.25 + 11y + y2 = 18.25 Factor a perfect square on the left side: (y + 5.5)(y + 5.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (y + 5.5) equal to 4.272001873 and -4.272001873.Subproblem 1
y + 5.5 = 4.272001873 Simplifying y + 5.5 = 4.272001873 Reorder the terms: 5.5 + y = 4.272001873 Solving 5.5 + y = 4.272001873 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + y = 4.272001873 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + y = 4.272001873 + -5.5 y = 4.272001873 + -5.5 Combine like terms: 4.272001873 + -5.5 = -1.227998127 y = -1.227998127 Simplifying y = -1.227998127Subproblem 2
y + 5.5 = -4.272001873 Simplifying y + 5.5 = -4.272001873 Reorder the terms: 5.5 + y = -4.272001873 Solving 5.5 + y = -4.272001873 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + y = -4.272001873 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + y = -4.272001873 + -5.5 y = -4.272001873 + -5.5 Combine like terms: -4.272001873 + -5.5 = -9.772001873 y = -9.772001873 Simplifying y = -9.772001873Solution
The solution to the problem is based on the solutions from the subproblems. y = {-1.227998127, -9.772001873}Solution
y = {0, -1.227998127, -9.772001873}
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