z^4-0.4096=0

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Solution for z^4-0.4096=0 equation:


Simplifying
z4 + -0.4096 = 0

Reorder the terms:
-0.4096 + z4 = 0

Solving
-0.4096 + z4 = 0

Solving for variable 'z'.

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

Add '0.4096' to each side of the equation.
-0.4096 + 0.4096 + z4 = 0 + 0.4096

Combine like terms: -0.4096 + 0.4096 = 0.0000
0.0000 + z4 = 0 + 0.4096
z4 = 0 + 0.4096

Combine like terms: 0 + 0.4096 = 0.4096
z4 = 0.4096

Simplifying
z4 = 0.4096

Reorder the terms:
-0.4096 + z4 = 0.4096 + -0.4096

Combine like terms: 0.4096 + -0.4096 = 0.0000
-0.4096 + z4 = 0.0000

Factor a difference between two squares.
(0.64 + z2)(-0.64 + z2) = 0.0000

Factor a difference between two squares.
(0.64 + z2)((0.8 + z)(-0.8 + z)) = 0.0000

Subproblem 1

Set the factor '(0.64 + z2)' equal to zero and attempt to solve: Simplifying 0.64 + z2 = 0 Solving 0.64 + z2 = 0 Move all terms containing z to the left, all other terms to the right. Add '-0.64' to each side of the equation. 0.64 + -0.64 + z2 = 0 + -0.64 Combine like terms: 0.64 + -0.64 = 0.00 0.00 + z2 = 0 + -0.64 z2 = 0 + -0.64 Combine like terms: 0 + -0.64 = -0.64 z2 = -0.64 Simplifying z2 = -0.64 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 '(0.8 + z)' equal to zero and attempt to solve: Simplifying 0.8 + z = 0 Solving 0.8 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + z = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + z = 0 + -0.8 z = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 z = -0.8 Simplifying z = -0.8

Subproblem 3

Set the factor '(-0.8 + z)' equal to zero and attempt to solve: Simplifying -0.8 + z = 0 Solving -0.8 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + z = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + z = 0 + 0.8 z = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 z = 0.8 Simplifying z = 0.8

Solution

z = {-0.8, 0.8}

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