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Simplifying y4 + 2y2 = 99 Reorder the terms: 2y2 + y4 = 99 Solving 2y2 + y4 = 99 Solving for variable 'y'. Reorder the terms: -99 + 2y2 + y4 = 99 + -99 Combine like terms: 99 + -99 = 0 -99 + 2y2 + y4 = 0 Factor a trinomial. (-11 + -1y2)(9 + -1y2) = 0 Factor a difference between two squares. (-11 + -1y2)((3 + y)(3 + -1y)) = 0Subproblem 1
Set the factor '(-11 + -1y2)' equal to zero and attempt to solve: Simplifying -11 + -1y2 = 0 Solving -11 + -1y2 = 0 Move all terms containing y to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -1y2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -1y2 = 0 + 11 -1y2 = 0 + 11 Combine like terms: 0 + 11 = 11 -1y2 = 11 Divide each side by '-1'. y2 = -11 Simplifying y2 = -11 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 '(3 + y)' equal to zero and attempt to solve: Simplifying 3 + y = 0 Solving 3 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + y = 0 + -3 y = 0 + -3 Combine like terms: 0 + -3 = -3 y = -3 Simplifying y = -3Subproblem 3
Set the factor '(3 + -1y)' equal to zero and attempt to solve: Simplifying 3 + -1y = 0 Solving 3 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1y = 0 + -3 -1y = 0 + -3 Combine like terms: 0 + -3 = -3 -1y = -3 Divide each side by '-1'. y = 3 Simplifying y = 3Solution
y = {-3, 3}
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