1. **State the problem:** Find the $x$-value on the curve $y = x^2$ where the tangent line is parallel to the line $y = 2x - 4$. 2. **Identify the slope of the given line:** The line $y = 2x - 4$ has slope $m = 2$. 3. **Find the derivative of the curve:** The derivative $y' = \frac{dy}{dx}$ gives the slope of the tangent line at any point on the curve. $$y = x^2 \implies y' = 2x$$ 4. **Set the slope of the tangent equal to the slope of the given line:** $$2x = 2$$ 5. **Solve for $x$:** $$x = 1$$ 6. **Conclusion:** The tangent to the curve $y = x^2$ is parallel to $y = 2x - 4$ at $x = 1$.