500x^4-x^2=0

Solution for 500x^4-x^2=0 equation:

Simplifying
500x4 + -1x2 = 0

Reorder the terms:
-1x2 + 500x4 = 0

Solving
-1x2 + 500x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-1 + 500x2) = 0

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(-1 + 500x2)' equal to zero and attempt to solve:

Simplifying
-1 + 500x2 = 0

Solving
-1 + 500x2 = 0

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

Add '1' to each side of the equation.
-1 + 1 + 500x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 500x2 = 0 + 1
500x2 = 0 + 1

Combine like terms: 0 + 1 = 1
500x2 = 1

Divide each side by '500'.
x2 = 0.002

Simplifying
x2 = 0.002

Take the square root of each side:
x = {-0.04472136, 0.04472136}
Solution
x = {0, -0.04472136, 0.04472136}