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Simplifying 3y3 + 24y2 + 9y = 0 Reorder the terms: 9y + 24y2 + 3y3 = 0 Solving 9y + 24y2 + 3y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3y'. 3y(3 + 8y + 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 + 8y + y2)' equal to zero and attempt to solve: Simplifying 3 + 8y + y2 = 0 Solving 3 + 8y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 8y + -3 + y2 = 0 + -3 Reorder the terms: 3 + -3 + 8y + y2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 8y + y2 = 0 + -3 8y + y2 = 0 + -3 Combine like terms: 0 + -3 = -3 8y + y2 = -3 The y term is 8y. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8y + 16 + y2 = -3 + 16 Reorder the terms: 16 + 8y + y2 = -3 + 16 Combine like terms: -3 + 16 = 13 16 + 8y + y2 = 13 Factor a perfect square on the left side: (y + 4)(y + 4) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (y + 4) equal to 3.605551275 and -3.605551275.Subproblem 1
y + 4 = 3.605551275 Simplifying y + 4 = 3.605551275 Reorder the terms: 4 + y = 3.605551275 Solving 4 + y = 3.605551275 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = 3.605551275 + -4 Combine like terms: 4 + -4 = 0 0 + y = 3.605551275 + -4 y = 3.605551275 + -4 Combine like terms: 3.605551275 + -4 = -0.394448725 y = -0.394448725 Simplifying y = -0.394448725Subproblem 2
y + 4 = -3.605551275 Simplifying y + 4 = -3.605551275 Reorder the terms: 4 + y = -3.605551275 Solving 4 + y = -3.605551275 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = -3.605551275 + -4 Combine like terms: 4 + -4 = 0 0 + y = -3.605551275 + -4 y = -3.605551275 + -4 Combine like terms: -3.605551275 + -4 = -7.605551275 y = -7.605551275 Simplifying y = -7.605551275Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.394448725, -7.605551275}Solution
y = {0, -0.394448725, -7.605551275}
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