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Simplifying y3 + -10y2 + -21y = 0 Reorder the terms: -21y + -10y2 + y3 = 0 Solving -21y + -10y2 + y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(-21 + -10y + 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 '(-21 + -10y + y2)' equal to zero and attempt to solve: Simplifying -21 + -10y + y2 = 0 Solving -21 + -10y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + -10y + 21 + y2 = 0 + 21 Reorder the terms: -21 + 21 + -10y + y2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -10y + y2 = 0 + 21 -10y + y2 = 0 + 21 Combine like terms: 0 + 21 = 21 -10y + y2 = 21 The y term is -10y. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10y + 25 + y2 = 21 + 25 Reorder the terms: 25 + -10y + y2 = 21 + 25 Combine like terms: 21 + 25 = 46 25 + -10y + y2 = 46 Factor a perfect square on the left side: (y + -5)(y + -5) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (y + -5) equal to 6.782329983 and -6.782329983.Subproblem 1
y + -5 = 6.782329983 Simplifying y + -5 = 6.782329983 Reorder the terms: -5 + y = 6.782329983 Solving -5 + y = 6.782329983 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = 6.782329983 + 5 Combine like terms: -5 + 5 = 0 0 + y = 6.782329983 + 5 y = 6.782329983 + 5 Combine like terms: 6.782329983 + 5 = 11.782329983 y = 11.782329983 Simplifying y = 11.782329983Subproblem 2
y + -5 = -6.782329983 Simplifying y + -5 = -6.782329983 Reorder the terms: -5 + y = -6.782329983 Solving -5 + y = -6.782329983 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = -6.782329983 + 5 Combine like terms: -5 + 5 = 0 0 + y = -6.782329983 + 5 y = -6.782329983 + 5 Combine like terms: -6.782329983 + 5 = -1.782329983 y = -1.782329983 Simplifying y = -1.782329983Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.782329983, -1.782329983}Solution
y = {0, 11.782329983, -1.782329983}
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