x^4+16x^2-512=0

Solution for x^4+16x^2-512=0 equation:

Simplifying
x4 + 16x2 + -512 = 0

Reorder the terms:
-512 + 16x2 + x4 = 0

Solving
-512 + 16x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-32 + -1x2)(16 + -1x2) = 0

Factor a difference between two squares.
(-32 + -1x2)((4 + x)(4 + -1x)) = 0

Subproblem 1
Set the factor '(-32 + -1x2)' equal to zero and attempt to solve:

Simplifying
-32 + -1x2 = 0

Solving
-32 + -1x2 = 0

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

Add '32' to each side of the equation.
-32 + 32 + -1x2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -1x2 = 0 + 32
-1x2 = 0 + 32

Combine like terms: 0 + 32 = 32
-1x2 = 32

Divide each side by '-1'.
x2 = -32

Simplifying
x2 = -32

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

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-4, 4}