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Simplifying z8 + -15z4 + -16 = 0 Reorder the terms: -16 + -15z4 + z8 = 0 Solving -16 + -15z4 + z8 = 0 Solving for variable 'z'. Factor a trinomial. (-1 + -1z4)(16 + -1z4) = 0 Factor a difference between two squares. (-1 + -1z4)((4 + z2)(4 + -1z2)) = 0 Factor a difference between two squares. (-1 + -1z4)((4 + z2)((2 + z)(2 + -1z))) = 0Subproblem 1
Set the factor '(-1 + -1z4)' equal to zero and attempt to solve: Simplifying -1 + -1z4 = 0 Solving -1 + -1z4 = 0 Move all terms containing z to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1z4 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1z4 = 0 + 1 -1z4 = 0 + 1 Combine like terms: 0 + 1 = 1 -1z4 = 1 Divide each side by '-1'. z4 = -1 Simplifying z4 = -1 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 + z2)' equal to zero and attempt to solve: Simplifying 4 + z2 = 0 Solving 4 + z2 = 0 Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + z2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + z2 = 0 + -4 z2 = 0 + -4 Combine like terms: 0 + -4 = -4 z2 = -4 Simplifying z2 = -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 + z)' equal to zero and attempt to solve: Simplifying 2 + z = 0 Solving 2 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + z = 0 + -2 z = 0 + -2 Combine like terms: 0 + -2 = -2 z = -2 Simplifying z = -2Subproblem 4
Set the factor '(2 + -1z)' equal to zero and attempt to solve: Simplifying 2 + -1z = 0 Solving 2 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1z = 0 + -2 -1z = 0 + -2 Combine like terms: 0 + -2 = -2 -1z = -2 Divide each side by '-1'. z = 2 Simplifying z = 2Solution
z = {-2, 2}
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