0=x^4-2x^2-8

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Solution for 0=x^4-2x^2-8 equation: 


Simplifying
0 = x4 + -2x2 + -8

Reorder the terms:
0 = -8 + -2x2 + x4

Solving
0 = -8 + -2x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + 8 = 8
8 + 2x2 + -1x4 = -8 + -2x2 + x4 + 8 + 2x2 + -1x4

Reorder the terms:
8 + 2x2 + -1x4 = -8 + 8 + -2x2 + 2x2 + x4 + -1x4

Combine like terms: -8 + 8 = 0
8 + 2x2 + -1x4 = 0 + -2x2 + 2x2 + x4 + -1x4
8 + 2x2 + -1x4 = -2x2 + 2x2 + x4 + -1x4

Combine like terms: -2x2 + 2x2 = 0
8 + 2x2 + -1x4 = 0 + x4 + -1x4
8 + 2x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
8 + 2x2 + -1x4 = 0

Factor a trinomial.
(4 + -1x2)(2 + x2) = 0

Factor a difference between two squares.
((2 + x)(2 + -1x))(2 + x2) = 0


Subproblem 1
Set the factor '(2 + x2)' equal to zero and attempt to solve:

Simplifying
2 + x2 = 0

Solving
2 + x2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x2 = 0 + -2
x2 = 0 + -2

Combine like terms: 0 + -2 = -2
x2 = -2

Simplifying
x2 = -2

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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2

Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-2, 2}

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