Let's solve the equation \(8x^{-2} = \frac{2}{25}\) for x. We can rewrite the equation as \(\frac{8}{x^2} = \frac{2}{25}\). Cross-multiplying, we get \(8 \times 25 = 2x^2\), which simplifies to \(200 = 2x^2\). 

Dividing both sides by 2, we get \(100 = x^2\). 

Taking the square root of both sides, we find that \(x = \pm 10\). So the solutions to the equation are x = 10 and x = -10.