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Simplifying y3 + -18y2 + -48y = 0 Reorder the terms: -48y + -18y2 + y3 = 0 Solving -48y + -18y2 + y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(-48 + -18y + 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 '(-48 + -18y + y2)' equal to zero and attempt to solve: Simplifying -48 + -18y + y2 = 0 Solving -48 + -18y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + -18y + 48 + y2 = 0 + 48 Reorder the terms: -48 + 48 + -18y + y2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -18y + y2 = 0 + 48 -18y + y2 = 0 + 48 Combine like terms: 0 + 48 = 48 -18y + y2 = 48 The y term is -18y. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18y + 81 + y2 = 48 + 81 Reorder the terms: 81 + -18y + y2 = 48 + 81 Combine like terms: 48 + 81 = 129 81 + -18y + y2 = 129 Factor a perfect square on the left side: (y + -9)(y + -9) = 129 Calculate the square root of the right side: 11.357816692 Break this problem into two subproblems by setting (y + -9) equal to 11.357816692 and -11.357816692.Subproblem 1
y + -9 = 11.357816692 Simplifying y + -9 = 11.357816692 Reorder the terms: -9 + y = 11.357816692 Solving -9 + y = 11.357816692 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + y = 11.357816692 + 9 Combine like terms: -9 + 9 = 0 0 + y = 11.357816692 + 9 y = 11.357816692 + 9 Combine like terms: 11.357816692 + 9 = 20.357816692 y = 20.357816692 Simplifying y = 20.357816692Subproblem 2
y + -9 = -11.357816692 Simplifying y + -9 = -11.357816692 Reorder the terms: -9 + y = -11.357816692 Solving -9 + y = -11.357816692 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + y = -11.357816692 + 9 Combine like terms: -9 + 9 = 0 0 + y = -11.357816692 + 9 y = -11.357816692 + 9 Combine like terms: -11.357816692 + 9 = -2.357816692 y = -2.357816692 Simplifying y = -2.357816692Solution
The solution to the problem is based on the solutions from the subproblems. y = {20.357816692, -2.357816692}Solution
y = {0, 20.357816692, -2.357816692}
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