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Simplifying z4 + -10z2 = 96 Reorder the terms: -10z2 + z4 = 96 Solving -10z2 + z4 = 96 Solving for variable 'z'. Reorder the terms: -96 + -10z2 + z4 = 96 + -96 Combine like terms: 96 + -96 = 0 -96 + -10z2 + z4 = 0 Factor a trinomial. (-6 + -1z2)(16 + -1z2) = 0 Factor a difference between two squares. (-6 + -1z2)((4 + z)(4 + -1z)) = 0Subproblem 1
Set the factor '(-6 + -1z2)' equal to zero and attempt to solve: Simplifying -6 + -1z2 = 0 Solving -6 + -1z2 = 0 Move all terms containing z to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1z2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1z2 = 0 + 6 -1z2 = 0 + 6 Combine like terms: 0 + 6 = 6 -1z2 = 6 Divide each side by '-1'. z2 = -6 Simplifying z2 = -6 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 + z)' equal to zero and attempt to solve: Simplifying 4 + z = 0 Solving 4 + z = 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 + z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + z = 0 + -4 z = 0 + -4 Combine like terms: 0 + -4 = -4 z = -4 Simplifying z = -4Subproblem 3
Set the factor '(4 + -1z)' equal to zero and attempt to solve: Simplifying 4 + -1z = 0 Solving 4 + -1z = 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 + -1z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1z = 0 + -4 -1z = 0 + -4 Combine like terms: 0 + -4 = -4 -1z = -4 Divide each side by '-1'. z = 4 Simplifying z = 4Solution
z = {-4, 4}
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