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Simplifying y4 + -13y2 + 35 = 0 Reorder the terms: 35 + -13y2 + y4 = 0 Solving 35 + -13y2 + y4 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-35' to each side of the equation. 35 + -13y2 + -35 + y4 = 0 + -35 Reorder the terms: 35 + -35 + -13y2 + y4 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + -13y2 + y4 = 0 + -35 -13y2 + y4 = 0 + -35 Combine like terms: 0 + -35 = -35 -13y2 + y4 = -35 The y term is -13y2. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13y2 + 42.25 + y4 = -35 + 42.25 Reorder the terms: 42.25 + -13y2 + y4 = -35 + 42.25 Combine like terms: -35 + 42.25 = 7.25 42.25 + -13y2 + y4 = 7.25 Factor a perfect square on the left side: (y2 + -6.5)(y2 + -6.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (y2 + -6.5) equal to 2.692582404 and -2.692582404.Subproblem 1
y2 + -6.5 = 2.692582404 Simplifying y2 + -6.5 = 2.692582404 Reorder the terms: -6.5 + y2 = 2.692582404 Solving -6.5 + y2 = 2.692582404 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + y2 = 2.692582404 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + y2 = 2.692582404 + 6.5 y2 = 2.692582404 + 6.5 Combine like terms: 2.692582404 + 6.5 = 9.192582404 y2 = 9.192582404 Simplifying y2 = 9.192582404 Take the square root of each side: y = {-3.031927177, 3.031927177}Subproblem 2
y2 + -6.5 = -2.692582404 Simplifying y2 + -6.5 = -2.692582404 Reorder the terms: -6.5 + y2 = -2.692582404 Solving -6.5 + y2 = -2.692582404 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + y2 = -2.692582404 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + y2 = -2.692582404 + 6.5 y2 = -2.692582404 + 6.5 Combine like terms: -2.692582404 + 6.5 = 3.807417596 y2 = 3.807417596 Simplifying y2 = 3.807417596 Take the square root of each side: y = {-1.951260515, 1.951260515}Solution
The solution to the problem is based on the solutions from the subproblems. y = {-3.031927177, 3.031927177, -1.951260515, 1.951260515}
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