1. The problem is to simplify the expression $\frac{1}{2}x^2 + x$. 2. Notice that the expression contains two terms: $\frac{1}{2}x^2$ and $x$. 3. We can factor out the common factor $x$ from both terms: $$\frac{1}{2}x^2 + x = x\left(\frac{1}{2}x + 1\right)$$ 4. This is the simplified form of the expression. Final answer: $$x\left(\frac{1}{2}x + 1\right)$$