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Simplifying z16 = 256 Solving z16 = 256 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Simplifying z16 = 256 Reorder the terms: -256 + z16 = 256 + -256 Combine like terms: 256 + -256 = 0 -256 + z16 = 0 Factor a difference between two squares. (16 + z8)(-16 + z8) = 0 Factor a difference between two squares. (16 + z8)((4 + z4)(-4 + z4)) = 0 Factor a difference between two squares. (16 + z8)((4 + z4)((2 + z2)(-2 + z2))) = 0Subproblem 1
Set the factor '(16 + z8)' equal to zero and attempt to solve: Simplifying 16 + z8 = 0 Solving 16 + z8 = 0 Move all terms containing z to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + z8 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + z8 = 0 + -16 z8 = 0 + -16 Combine like terms: 0 + -16 = -16 z8 = -16 Simplifying z8 = -16 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 + z4)' equal to zero and attempt to solve: Simplifying 4 + z4 = 0 Solving 4 + z4 = 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 + z4 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + z4 = 0 + -4 z4 = 0 + -4 Combine like terms: 0 + -4 = -4 z4 = -4 Simplifying z4 = -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 + z2)' equal to zero and attempt to solve: Simplifying 2 + z2 = 0 Solving 2 + z2 = 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 + z2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + z2 = 0 + -2 z2 = 0 + -2 Combine like terms: 0 + -2 = -2 z2 = -2 Simplifying z2 = -2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 4
Set the factor '(-2 + z2)' equal to zero and attempt to solve: Simplifying -2 + z2 = 0 Solving -2 + z2 = 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 + z2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + z2 = 0 + 2 z2 = 0 + 2 Combine like terms: 0 + 2 = 2 z2 = 2 Simplifying z2 = 2 Take the square root of each side: z = {-1.414213562, 1.414213562}Solution
z = {-1.414213562, 1.414213562}
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