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Simplifying x8 + -21x4 + 80 = 0 Reorder the terms: 80 + -21x4 + x8 = 0 Solving 80 + -21x4 + x8 = 0 Solving for variable 'x'. Factor a trinomial. (5 + -1x4)(16 + -1x4) = 0 Factor a difference between two squares. (5 + -1x4)((4 + x2)(4 + -1x2)) = 0 Factor a difference between two squares. (5 + -1x4)((4 + x2)((2 + x)(2 + -1x))) = 0Subproblem 1
Set the factor '(5 + -1x4)' equal to zero and attempt to solve: Simplifying 5 + -1x4 = 0 Solving 5 + -1x4 = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x4 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x4 = 0 + -5 -1x4 = 0 + -5 Combine like terms: 0 + -5 = -5 -1x4 = -5 Divide each side by '-1'. x4 = 5 Simplifying x4 = 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 '(4 + x2)' equal to zero and attempt to solve: Simplifying 4 + x2 = 0 Solving 4 + x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = 0 + -4 x2 = 0 + -4 Combine like terms: 0 + -4 = -4 x2 = -4 Simplifying x2 = -4 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 4
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-2, 2}
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