1. **State the problem:** Solve the equation $2x - \frac{2}{x^2} = 0$ for $x$. 2. **Rewrite the equation:** Move terms to isolate fractions: $$2x = \frac{2}{x^2}$$ 3. **Multiply both sides by $x^2$ to clear the denominator:** $$2x \cdot x^2 = 2$$ $$2x^3 = 2$$ 4. **Divide both sides by 2:** $$x^3 = 1$$ 5. **Solve for $x$ by taking the cube root:** $$x = \sqrt[3]{1} = 1$$ 6. **Check for extraneous solutions:** Since $x=1$ does not make any denominator zero, it is valid. **Final answer:** $$x = 1$$