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Simplifying y3 = 15y + 8y2 Solving y3 = 15y + 8y2 Solving for variable 'y'. Reorder the terms: -15y + -8y2 + y3 = 15y + 8y2 + -15y + -8y2 Reorder the terms: -15y + -8y2 + y3 = 15y + -15y + 8y2 + -8y2 Combine like terms: 15y + -15y = 0 -15y + -8y2 + y3 = 0 + 8y2 + -8y2 -15y + -8y2 + y3 = 8y2 + -8y2 Combine like terms: 8y2 + -8y2 = 0 -15y + -8y2 + y3 = 0 Factor out the Greatest Common Factor (GCF), 'y'. y(-15 + -8y + 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 '(-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 = 9.567764363 y = 9.567764363 Simplifying y = 9.567764363Subproblem 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 = -1.567764363 y = -1.567764363 Simplifying y = -1.567764363Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.567764363, -1.567764363}Solution
y = {0, 9.567764363, -1.567764363}
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