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Simplifying 3y3 + 24y2 + -45y = 0 Reorder the terms: -45y + 24y2 + 3y3 = 0 Solving -45y + 24y2 + 3y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3y'. 3y(-15 + 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 '(-15 + 8y + y2)' equal to zero and attempt to solve: Simplifying -15 + 8y + y2 = 0 Solving -15 + 8y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 8y + 15 + y2 = 0 + 15 Reorder the terms: -15 + 15 + 8y + y2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 8y + y2 = 0 + 15 8y + y2 = 0 + 15 Combine like terms: 0 + 15 = 15 8y + y2 = 15 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 = 15 + 16 Reorder the terms: 16 + 8y + y2 = 15 + 16 Combine like terms: 15 + 16 = 31 16 + 8y + y2 = 31 Factor a perfect square on the left side: (y + 4)(y + 4) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (y + 4) equal to 5.567764363 and -5.567764363.Subproblem 1
y + 4 = 5.567764363 Simplifying y + 4 = 5.567764363 Reorder the terms: 4 + y = 5.567764363 Solving 4 + y = 5.567764363 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 = 5.567764363 + -4 Combine like terms: 4 + -4 = 0 0 + y = 5.567764363 + -4 y = 5.567764363 + -4 Combine like terms: 5.567764363 + -4 = 1.567764363 y = 1.567764363 Simplifying y = 1.567764363Subproblem 2
y + 4 = -5.567764363 Simplifying y + 4 = -5.567764363 Reorder the terms: 4 + y = -5.567764363 Solving 4 + y = -5.567764363 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 = -5.567764363 + -4 Combine like terms: 4 + -4 = 0 0 + y = -5.567764363 + -4 y = -5.567764363 + -4 Combine like terms: -5.567764363 + -4 = -9.567764363 y = -9.567764363 Simplifying y = -9.567764363Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.567764363, -9.567764363}Solution
y = {0, 1.567764363, -9.567764363}
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