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Simplifying 4y4 + -24y3 + -72y2 = 0 Reorder the terms: -72y2 + -24y3 + 4y4 = 0 Solving -72y2 + -24y3 + 4y4 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '4y2'. 4y2(-18 + -6y + y2) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve: Simplifying y2 = 0 Solving y2 = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y2 = 0 Take the square root of each side: y = {0}Subproblem 2
Set the factor '(-18 + -6y + y2)' equal to zero and attempt to solve: Simplifying -18 + -6y + y2 = 0 Solving -18 + -6y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -6y + 18 + y2 = 0 + 18 Reorder the terms: -18 + 18 + -6y + y2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -6y + y2 = 0 + 18 -6y + y2 = 0 + 18 Combine like terms: 0 + 18 = 18 -6y + y2 = 18 The y term is -6y. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6y + 9 + y2 = 18 + 9 Reorder the terms: 9 + -6y + y2 = 18 + 9 Combine like terms: 18 + 9 = 27 9 + -6y + y2 = 27 Factor a perfect square on the left side: (y + -3)(y + -3) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (y + -3) equal to 5.196152423 and -5.196152423.Subproblem 1
y + -3 = 5.196152423 Simplifying y + -3 = 5.196152423 Reorder the terms: -3 + y = 5.196152423 Solving -3 + y = 5.196152423 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = 5.196152423 + 3 Combine like terms: -3 + 3 = 0 0 + y = 5.196152423 + 3 y = 5.196152423 + 3 Combine like terms: 5.196152423 + 3 = 8.196152423 y = 8.196152423 Simplifying y = 8.196152423Subproblem 2
y + -3 = -5.196152423 Simplifying y + -3 = -5.196152423 Reorder the terms: -3 + y = -5.196152423 Solving -3 + y = -5.196152423 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = -5.196152423 + 3 Combine like terms: -3 + 3 = 0 0 + y = -5.196152423 + 3 y = -5.196152423 + 3 Combine like terms: -5.196152423 + 3 = -2.196152423 y = -2.196152423 Simplifying y = -2.196152423Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.196152423, -2.196152423}Solution
y = {0, 8.196152423, -2.196152423}
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