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Simplifying y5 + -16y4 + 16y3 = 0 Reorder the terms: 16y3 + -16y4 + y5 = 0 Solving 16y3 + -16y4 + y5 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y3'. y3(16 + -16y + 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 '(16 + -16y + y2)' equal to zero and attempt to solve: Simplifying 16 + -16y + y2 = 0 Solving 16 + -16y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + -16y + -16 + y2 = 0 + -16 Reorder the terms: 16 + -16 + -16y + y2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -16y + y2 = 0 + -16 -16y + y2 = 0 + -16 Combine like terms: 0 + -16 = -16 -16y + y2 = -16 The y term is -16y. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16y + 64 + y2 = -16 + 64 Reorder the terms: 64 + -16y + y2 = -16 + 64 Combine like terms: -16 + 64 = 48 64 + -16y + y2 = 48 Factor a perfect square on the left side: (y + -8)(y + -8) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (y + -8) equal to 6.92820323 and -6.92820323.Subproblem 1
y + -8 = 6.92820323 Simplifying y + -8 = 6.92820323 Reorder the terms: -8 + y = 6.92820323 Solving -8 + y = 6.92820323 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + y = 6.92820323 + 8 Combine like terms: -8 + 8 = 0 0 + y = 6.92820323 + 8 y = 6.92820323 + 8 Combine like terms: 6.92820323 + 8 = 14.92820323 y = 14.92820323 Simplifying y = 14.92820323Subproblem 2
y + -8 = -6.92820323 Simplifying y + -8 = -6.92820323 Reorder the terms: -8 + y = -6.92820323 Solving -8 + y = -6.92820323 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + y = -6.92820323 + 8 Combine like terms: -8 + 8 = 0 0 + y = -6.92820323 + 8 y = -6.92820323 + 8 Combine like terms: -6.92820323 + 8 = 1.07179677 y = 1.07179677 Simplifying y = 1.07179677Solution
The solution to the problem is based on the solutions from the subproblems. y = {14.92820323, 1.07179677}Solution
y = {14.92820323, 1.07179677}
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