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Simplifying y5 + -12y4 + 16y3 = 0 Reorder the terms: 16y3 + -12y4 + y5 = 0 Solving 16y3 + -12y4 + y5 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y3'. y3(16 + -12y + 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 + -12y + y2)' equal to zero and attempt to solve: Simplifying 16 + -12y + y2 = 0 Solving 16 + -12y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + -12y + -16 + y2 = 0 + -16 Reorder the terms: 16 + -16 + -12y + y2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -12y + y2 = 0 + -16 -12y + y2 = 0 + -16 Combine like terms: 0 + -16 = -16 -12y + y2 = -16 The y term is -12y. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12y + 36 + y2 = -16 + 36 Reorder the terms: 36 + -12y + y2 = -16 + 36 Combine like terms: -16 + 36 = 20 36 + -12y + y2 = 20 Factor a perfect square on the left side: (y + -6)(y + -6) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (y + -6) equal to 4.472135955 and -4.472135955.Subproblem 1
y + -6 = 4.472135955 Simplifying y + -6 = 4.472135955 Reorder the terms: -6 + y = 4.472135955 Solving -6 + y = 4.472135955 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = 4.472135955 + 6 Combine like terms: -6 + 6 = 0 0 + y = 4.472135955 + 6 y = 4.472135955 + 6 Combine like terms: 4.472135955 + 6 = 10.472135955 y = 10.472135955 Simplifying y = 10.472135955Subproblem 2
y + -6 = -4.472135955 Simplifying y + -6 = -4.472135955 Reorder the terms: -6 + y = -4.472135955 Solving -6 + y = -4.472135955 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = -4.472135955 + 6 Combine like terms: -6 + 6 = 0 0 + y = -4.472135955 + 6 y = -4.472135955 + 6 Combine like terms: -4.472135955 + 6 = 1.527864045 y = 1.527864045 Simplifying y = 1.527864045Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.472135955, 1.527864045}Solution
y = {10.472135955, 1.527864045}
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