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Simplifying 3y3 + -9y + 27y2 = 0 Reorder the terms: -9y + 27y2 + 3y3 = 0 Solving -9y + 27y2 + 3y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3y'. 3y(-3 + 9y + y2) = 0 Ignore the factor 3.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 '(-3 + 9y + y2)' equal to zero and attempt to solve: Simplifying -3 + 9y + y2 = 0 Solving -3 + 9y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 9y + 3 + y2 = 0 + 3 Reorder the terms: -3 + 3 + 9y + y2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 9y + y2 = 0 + 3 9y + y2 = 0 + 3 Combine like terms: 0 + 3 = 3 9y + y2 = 3 The y term is 9y. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9y + 20.25 + y2 = 3 + 20.25 Reorder the terms: 20.25 + 9y + y2 = 3 + 20.25 Combine like terms: 3 + 20.25 = 23.25 20.25 + 9y + y2 = 23.25 Factor a perfect square on the left side: (y + 4.5)(y + 4.5) = 23.25 Calculate the square root of the right side: 4.82182538 Break this problem into two subproblems by setting (y + 4.5) equal to 4.82182538 and -4.82182538.Subproblem 1
y + 4.5 = 4.82182538 Simplifying y + 4.5 = 4.82182538 Reorder the terms: 4.5 + y = 4.82182538 Solving 4.5 + y = 4.82182538 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + y = 4.82182538 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + y = 4.82182538 + -4.5 y = 4.82182538 + -4.5 Combine like terms: 4.82182538 + -4.5 = 0.32182538 y = 0.32182538 Simplifying y = 0.32182538Subproblem 2
y + 4.5 = -4.82182538 Simplifying y + 4.5 = -4.82182538 Reorder the terms: 4.5 + y = -4.82182538 Solving 4.5 + y = -4.82182538 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + y = -4.82182538 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + y = -4.82182538 + -4.5 y = -4.82182538 + -4.5 Combine like terms: -4.82182538 + -4.5 = -9.32182538 y = -9.32182538 Simplifying y = -9.32182538Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.32182538, -9.32182538}Solution
y = {0, 0.32182538, -9.32182538}
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