Z^4-9=0

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Solution for Z^4-9=0 equation:


Simplifying
Z4 + -9 = 0

Reorder the terms:
-9 + Z4 = 0

Solving
-9 + Z4 = 0

Solving for variable 'Z'.

Move all terms containing Z to the left, all other terms to the right.

Add '9' to each side of the equation.
-9 + 9 + Z4 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + Z4 = 0 + 9
Z4 = 0 + 9

Combine like terms: 0 + 9 = 9
Z4 = 9

Simplifying
Z4 = 9

Reorder the terms:
-9 + Z4 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + Z4 = 0

Factor a difference between two squares.
(3 + Z2)(-3 + Z2) = 0

Subproblem 1

Set the factor '(3 + Z2)' equal to zero and attempt to solve: Simplifying 3 + Z2 = 0 Solving 3 + Z2 = 0 Move all terms containing Z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + Z2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + Z2 = 0 + -3 Z2 = 0 + -3 Combine like terms: 0 + -3 = -3 Z2 = -3 Simplifying Z2 = -3 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 '(-3 + Z2)' equal to zero and attempt to solve: Simplifying -3 + Z2 = 0 Solving -3 + Z2 = 0 Move all terms containing Z to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + Z2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + Z2 = 0 + 3 Z2 = 0 + 3 Combine like terms: 0 + 3 = 3 Z2 = 3 Simplifying Z2 = 3 Take the square root of each side: Z = {-1.732050808, 1.732050808}

Solution

Z = {-1.732050808, 1.732050808}

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