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Simplifying y4 + -33y2 + 256 = 0 Reorder the terms: 256 + -33y2 + y4 = 0 Solving 256 + -33y2 + y4 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-256' to each side of the equation. 256 + -33y2 + -256 + y4 = 0 + -256 Reorder the terms: 256 + -256 + -33y2 + y4 = 0 + -256 Combine like terms: 256 + -256 = 0 0 + -33y2 + y4 = 0 + -256 -33y2 + y4 = 0 + -256 Combine like terms: 0 + -256 = -256 -33y2 + y4 = -256 The y term is -33y2. Take half its coefficient (-16.5). Square it (272.25) and add it to both sides. Add '272.25' to each side of the equation. -33y2 + 272.25 + y4 = -256 + 272.25 Reorder the terms: 272.25 + -33y2 + y4 = -256 + 272.25 Combine like terms: -256 + 272.25 = 16.25 272.25 + -33y2 + y4 = 16.25 Factor a perfect square on the left side: (y2 + -16.5)(y2 + -16.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (y2 + -16.5) equal to 4.031128874 and -4.031128874.Subproblem 1
y2 + -16.5 = 4.031128874 Simplifying y2 + -16.5 = 4.031128874 Reorder the terms: -16.5 + y2 = 4.031128874 Solving -16.5 + y2 = 4.031128874 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + y2 = 4.031128874 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + y2 = 4.031128874 + 16.5 y2 = 4.031128874 + 16.5 Combine like terms: 4.031128874 + 16.5 = 20.531128874 y2 = 20.531128874 Simplifying y2 = 20.531128874 Take the square root of each side: y = {-4.531128874, 4.531128874}Subproblem 2
y2 + -16.5 = -4.031128874 Simplifying y2 + -16.5 = -4.031128874 Reorder the terms: -16.5 + y2 = -4.031128874 Solving -16.5 + y2 = -4.031128874 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + y2 = -4.031128874 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + y2 = -4.031128874 + 16.5 y2 = -4.031128874 + 16.5 Combine like terms: -4.031128874 + 16.5 = 12.468871126 y2 = 12.468871126 Simplifying y2 = 12.468871126 Take the square root of each side: y = {-3.531128874, 3.531128874}Solution
The solution to the problem is based on the solutions from the subproblems. y = {-4.531128874, 4.531128874, -3.531128874, 3.531128874}
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