1. **State the problem:** Evaluate the expression $5x^2 + 2x + 6$ when $x=3$. 2. **Recall the formula:** The expression is a quadratic polynomial in $x$. 3. **Substitute the value:** Replace $x$ with 3 in the expression: $$5(3)^2 + 2(3) + 6$$ 4. **Calculate powers and products:** $$5 \times 9 + 2 \times 3 + 6 = 45 + 6 + 6$$ 5. **Add all terms:** $$45 + 6 + 6 = 57$$ 6. **Final answer:** The value of the expression when $x=3$ is **57**.