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Simplifying y4 + 9y2 + -100 = 0 Reorder the terms: -100 + 9y2 + y4 = 0 Solving -100 + 9y2 + y4 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 9y2 + 100 + y4 = 0 + 100 Reorder the terms: -100 + 100 + 9y2 + y4 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 9y2 + y4 = 0 + 100 9y2 + y4 = 0 + 100 Combine like terms: 0 + 100 = 100 9y2 + y4 = 100 The y term is 9y2. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9y2 + 20.25 + y4 = 100 + 20.25 Reorder the terms: 20.25 + 9y2 + y4 = 100 + 20.25 Combine like terms: 100 + 20.25 = 120.25 20.25 + 9y2 + y4 = 120.25 Factor a perfect square on the left side: (y2 + 4.5)(y2 + 4.5) = 120.25 Calculate the square root of the right side: 10.9658561 Break this problem into two subproblems by setting (y2 + 4.5) equal to 10.9658561 and -10.9658561.Subproblem 1
y2 + 4.5 = 10.9658561 Simplifying y2 + 4.5 = 10.9658561 Reorder the terms: 4.5 + y2 = 10.9658561 Solving 4.5 + y2 = 10.9658561 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + y2 = 10.9658561 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + y2 = 10.9658561 + -4.5 y2 = 10.9658561 + -4.5 Combine like terms: 10.9658561 + -4.5 = 6.4658561 y2 = 6.4658561 Simplifying y2 = 6.4658561 Take the square root of each side: y = {-2.54280477, 2.54280477}Subproblem 2
y2 + 4.5 = -10.9658561 Simplifying y2 + 4.5 = -10.9658561 Reorder the terms: 4.5 + y2 = -10.9658561 Solving 4.5 + y2 = -10.9658561 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + y2 = -10.9658561 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + y2 = -10.9658561 + -4.5 y2 = -10.9658561 + -4.5 Combine like terms: -10.9658561 + -4.5 = -15.4658561 y2 = -15.4658561 Simplifying y2 = -15.4658561 Reorder the terms: 15.4658561 + y2 = -15.4658561 + 15.4658561 Combine like terms: -15.4658561 + 15.4658561 = 0.0000000 15.4658561 + y2 = 0.0000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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