Do negative words impact UX?

I'm interested to know if using negative words impacts the UX.

Let's say you have a headline for your website. Should you consider "We can help you" instead of "We solve problems" because the word "problems" is a negative one?

Just one word probably won't affect the user on a conscious level but maybe using this kind of language might create a mindset for your business and at the bottom of the page, the user might be affected.

If this statement is true, can we measure this effect on users?