1. **State the problem:** Solve the equation $$\frac{2x^{2} - 18x}{x} = 0$$ for $x$. 2. **Rewrite the equation:** The expression is a fraction equal to zero. A fraction equals zero if and only if its numerator is zero (and denominator is not zero). 3. **Set numerator equal to zero:** $$2x^{2} - 18x = 0$$ 4. **Factor the numerator:** $$2x(x - 9) = 0$$ 5. **Solve each factor:** - $2x = 0 \implies x = 0$ - $x - 9 = 0 \implies x = 9$ 6. **Check denominator:** The denominator is $x$, so $x \neq 0$ to avoid division by zero. 7. **Final solution:** Since $x=0$ is not allowed, the only solution is $$x = 9$$ Thus, the blank is correctly filled with $9$.