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Simplifying z4 + 8z2 + -9 = 0 Reorder the terms: -9 + 8z2 + z4 = 0 Solving -9 + 8z2 + z4 = 0 Solving for variable 'z'. Factor a trinomial. (-9 + -1z2)(1 + -1z2) = 0 Factor a difference between two squares. (-9 + -1z2)((1 + z)(1 + -1z)) = 0Subproblem 1
Set the factor '(-9 + -1z2)' equal to zero and attempt to solve: Simplifying -9 + -1z2 = 0 Solving -9 + -1z2 = 0 Move all terms containing z to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1z2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1z2 = 0 + 9 -1z2 = 0 + 9 Combine like terms: 0 + 9 = 9 -1z2 = 9 Divide each side by '-1'. z2 = -9 Simplifying z2 = -9 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 + z)' equal to zero and attempt to solve: Simplifying 1 + z = 0 Solving 1 + z = 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 + z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + z = 0 + -1 z = 0 + -1 Combine like terms: 0 + -1 = -1 z = -1 Simplifying z = -1Subproblem 3
Set the factor '(1 + -1z)' equal to zero and attempt to solve: Simplifying 1 + -1z = 0 Solving 1 + -1z = 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 + -1z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1z = 0 + -1 -1z = 0 + -1 Combine like terms: 0 + -1 = -1 -1z = -1 Divide each side by '-1'. z = 1 Simplifying z = 1Solution
z = {-1, 1}
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