Expanding $(x + y)^2$, we get $x^2 + 2xy + y^2 = 1$.
Substituting $xy = -4$, we have $x^2 + 2(-4) + y^2 = 1$.
Simplifying, we get $x^2 + y^2 = 1 + 8 = \boxed{9}$.
The answer is: 9
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
Given that $(x + y)^2 = 1$ and $xy = -4$, what is the value of $x^2 + y^2$?

### Answer:
