Vadim's answer handles the math (and I've upvoted it), so I will try to provide intuition.
The idea is the word "closer" is relative. That is, in some sense, $100{,}000$ is closer to $100{,}010$ than $1$ is to $0$. Of course, in an absolute sense, $1$ is $1$ away from $0$ while $100{,}000$ is $10$ away from $100{,}010$.
But, say you had $\$1$ and I took away $\$1$ and contrast that with the scenario where you have $\$100{,}010$ and I take $\$10$. In the second scenario, I take more money. But in the first scenario, you care a lot more about the theft.
In your particular example, something similar happens. Yes, $x^2 + x$ and $x^2$ have a very large difference when $x$ is large. But the relative difference is tiny. For example, when $x = 1{,}000$, then $x^2 + x = 1{,}001{,}000$ while $x^2 = 1{,}000{,}000$. So, yes, the difference is large (it's $1000$), but the relative difference is not that big - these two numbers are separated by a mere $0.1\%$ And this percentage shrinks as $x$ gets even bigger.