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Simplifying y5 + -18y4 + 6y3 = 0 Reorder the terms: 6y3 + -18y4 + y5 = 0 Solving 6y3 + -18y4 + y5 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y3'. y3(6 + -18y + y2) = 0Subproblem 1
Set the factor 'y3' equal to zero and attempt to solve: Simplifying y3 = 0 Solving y3 = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(6 + -18y + y2)' equal to zero and attempt to solve: Simplifying 6 + -18y + y2 = 0 Solving 6 + -18y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -18y + -6 + y2 = 0 + -6 Reorder the terms: 6 + -6 + -18y + y2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -18y + y2 = 0 + -6 -18y + y2 = 0 + -6 Combine like terms: 0 + -6 = -6 -18y + y2 = -6 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 = -6 + 81 Reorder the terms: 81 + -18y + y2 = -6 + 81 Combine like terms: -6 + 81 = 75 81 + -18y + y2 = 75 Factor a perfect square on the left side: (y + -9)(y + -9) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (y + -9) equal to 8.660254038 and -8.660254038.Subproblem 1
y + -9 = 8.660254038 Simplifying y + -9 = 8.660254038 Reorder the terms: -9 + y = 8.660254038 Solving -9 + y = 8.660254038 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 = 8.660254038 + 9 Combine like terms: -9 + 9 = 0 0 + y = 8.660254038 + 9 y = 8.660254038 + 9 Combine like terms: 8.660254038 + 9 = 17.660254038 y = 17.660254038 Simplifying y = 17.660254038Subproblem 2
y + -9 = -8.660254038 Simplifying y + -9 = -8.660254038 Reorder the terms: -9 + y = -8.660254038 Solving -9 + y = -8.660254038 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 = -8.660254038 + 9 Combine like terms: -9 + 9 = 0 0 + y = -8.660254038 + 9 y = -8.660254038 + 9 Combine like terms: -8.660254038 + 9 = 0.339745962 y = 0.339745962 Simplifying y = 0.339745962Solution
The solution to the problem is based on the solutions from the subproblems. y = {17.660254038, 0.339745962}Solution
y = {17.660254038, 0.339745962}
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