The sum of a negative integer $N$ and its square is 6. What is the value of $N$?
To solve for $N$, I need to find a number that satisfies the equation $N + N^2 = 6$. Since $N$ is negative, I'll start with $-1$. If $N = -1$, then $N + N^2 = -1 + 1 = 0$, which is not 6. So $-1$ is not the answer. I'll try $-2$ next. If $N = -2$, then $N + N^2 = -2 + 4 = 2$, which is also not 6. I'll keep going with $-3$. If $N = -3$, then $N + N^2 = -3 + 9 = 6$, which is exactly what I want. So $N = -3$ is the answer. 