x^2-.01x^4=0

Solution for x^2-.01x^4=0 equation:

Simplifying
x2 + -0.01x4 = 0

Solving
x2 + -0.01x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(1 + -0.01x2) = 0

Factor a difference between two squares.
x2((1 + 0.1x)(1 + -0.1x)) = 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 + 0.1x)' equal to zero and attempt to solve:

Simplifying
1 + 0.1x = 0

Solving
1 + 0.1x = 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 + 0.1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 0.1x = 0 + -1
0.1x = 0 + -1

Combine like terms: 0 + -1 = -1
0.1x = -1

Divide each side by '0.1'.
x = -10

Simplifying
x = -10
Subproblem 3
Set the factor '(1 + -0.1x)' equal to zero and attempt to solve:

Simplifying
1 + -0.1x = 0

Solving
1 + -0.1x = 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 + -0.1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -0.1x = 0 + -1
-0.1x = 0 + -1

Combine like terms: 0 + -1 = -1
-0.1x = -1

Divide each side by '-0.1'.
x = 10

Simplifying
x = 10
Solution
x = {0, -10, 10}