1. We are asked to express $x^2 + 4x + 1$ in the form $(x + a)^2 - b$ and then solve $x^2 + 4x + 1 = 0$. 2. To express $x^2 + 4x + 1$ in the form $(x + a)^2 - b$, we complete the square. 3. Recall the formula for completing the square: $$x^2 + 2ax + a^2 = (x + a)^2$$ 4. For $x^2 + 4x + 1$, compare $4x$ with $2ax$ to find $a$: $$2a = 4 \implies a = 2$$ 5. Now write: $$x^2 + 4x + 1 = (x + 2)^2 - (2^2 - 1) = (x + 2)^2 - (4 - 1) = (x + 2)^2 - 3$$ 6. So, $x^2 + 4x + 1 = (x + 2)^2 - 3$. 7. Next, solve $x^2 + 4x + 1 = 0$ using the completed square form: $$(x + 2)^2 - 3 = 0$$ 8. Add 3 to both sides: $$(x + 2)^2 = 3$$ 9. Take the square root of both sides: $$x + 2 = \pm \sqrt{3}$$ 10. Solve for $x$: $$x = -2 \pm \sqrt{3}$$ Final answer for part (b): $x = -2 + \sqrt{3}$ or $x = -2 - \sqrt{3}$. Note: The user asked to solve only the first question completely.