1. **State the problem:** Simplify the expression $x^2 + x^2$. 2. **Formula and rules:** When adding like terms, add their coefficients and keep the variable part the same. 3. **Intermediate work:** $$x^2 + x^2 = 1x^2 + 1x^2 = (1 + 1)x^2 = 2x^2$$ 4. **Explanation:** Since both terms have the same variable and exponent ($x^2$), we add their coefficients (1 + 1) to get 2, then multiply by $x^2$. 5. **Final answer:** $$2x^2$$