1. **State the problem:** Solve the equation $x = 2y + x^4$ for $y$ in terms of $x$. 2. **Rewrite the equation:** We want to isolate $y$ on one side. Starting with: $$x = 2y + x^4$$ 3. **Isolate $y$:** Subtract $x^4$ from both sides: $$x - x^4 = 2y$$ 4. **Divide both sides by 2:** $$y = \frac{x - x^4}{2}$$ 5. **Final answer:** $$y = \frac{x - x^4}{2}$$ This expresses $y$ explicitly in terms of $x$.