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Simplifying y4 + 4y2 + -5 = 0 Reorder the terms: -5 + 4y2 + y4 = 0 Solving -5 + 4y2 + y4 = 0 Solving for variable 'y'. Factor a trinomial. (-5 + -1y2)(1 + -1y2) = 0 Factor a difference between two squares. (-5 + -1y2)((1 + y)(1 + -1y)) = 0Subproblem 1
Set the factor '(-5 + -1y2)' equal to zero and attempt to solve: Simplifying -5 + -1y2 = 0 Solving -5 + -1y2 = 0 Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1y2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1y2 = 0 + 5 -1y2 = 0 + 5 Combine like terms: 0 + 5 = 5 -1y2 = 5 Divide each side by '-1'. y2 = -5 Simplifying y2 = -5 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 '(1 + y)' equal to zero and attempt to solve: Simplifying 1 + y = 0 Solving 1 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + y = 0 + -1 y = 0 + -1 Combine like terms: 0 + -1 = -1 y = -1 Simplifying y = -1Subproblem 3
Set the factor '(1 + -1y)' equal to zero and attempt to solve: Simplifying 1 + -1y = 0 Solving 1 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1y = 0 + -1 -1y = 0 + -1 Combine like terms: 0 + -1 = -1 -1y = -1 Divide each side by '-1'. y = 1 Simplifying y = 1Solution
y = {-1, 1}
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