1/2x4-8x2=0

To solve the equation \( \frac{1}{2} x^4 - 8x^2 = 0 \), we can proceed as follows:

1. Factor the equation:

   First, let's factor out the common term. Notice that both terms contain \( x^2 \):

   \[ \frac{1}{2} x^4 - 8x^2 = 0 \implies x^2 \left( \frac{1}{2} x^2 - 8 \right) = 0 \]

2. Set each factor equal to zero:

   We have two factors:

   \[ x^2 = 0 \quad \text{or} \quad \frac{1}{2} x^2 - 8 = 0 \]

   For the first factor: \[ x^2 = 0 \implies x = 0 \]

   For the second factor: \[ \frac{1}{2} x^2 - 8 = 0 \implies \frac{1}{2} x^2 = 8 \implies x^2 = 16 \]

   So, \[ x = 4 \quad \text{or} \quad x = -4 \]

3. Combine the solutions:

Thus, the solutions to the equation \( \frac{1}{2} x^4 - 8x^2 = 0 \) are:

\[ x = 0, \quad x = 4, \quad x = -4 \]