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Simplifying y4 + (9y2) + -52 = 0 Reorder the terms: -52 + (9y2) + y4 = 0 Solving -52 + (9y2) + y4 = 0 Solving for variable 'y'. Factor a trinomial. (-13 + -1y2)(4 + -1y2) = 0 Factor a difference between two squares. (-13 + -1y2)((2 + y)(2 + -1y)) = 0Subproblem 1
Set the factor '(-13 + -1y2)' equal to zero and attempt to solve: Simplifying -13 + -1y2 = 0 Solving -13 + -1y2 = 0 Move all terms containing y to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + -1y2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -1y2 = 0 + 13 -1y2 = 0 + 13 Combine like terms: 0 + 13 = 13 -1y2 = 13 Divide each side by '-1'. y2 = -13 Simplifying y2 = -13 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 '(2 + y)' equal to zero and attempt to solve: Simplifying 2 + y = 0 Solving 2 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + y = 0 + -2 y = 0 + -2 Combine like terms: 0 + -2 = -2 y = -2 Simplifying y = -2Subproblem 3
Set the factor '(2 + -1y)' equal to zero and attempt to solve: Simplifying 2 + -1y = 0 Solving 2 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1y = 0 + -2 -1y = 0 + -2 Combine like terms: 0 + -2 = -2 -1y = -2 Divide each side by '-1'. y = 2 Simplifying y = 2Solution
y = {-2, 2}
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