Unfortunately DNN only searches on complete words, not partial words.

At least that is my understanding of the functionality.

Assuming you talking about DNN 4.9.x here is a solution working with my site.

You have to change the Storec Proc GETSEARCHRESULTS

Search the Line
   AND (sw.Word = @Word)
and change it to
   AND (sw.Word like @Word)

This brings also e.g. carwash when you search for car.

For using the standard wildcards * for one or more character and ? for one character, you can use this line

   AND (sw.Word LIKE REPLACE(REPLACE(@Word, '*', '%'),'?', '_'))

Of course you have to have administrative rights on your DB-Server. So, if you have your DNN running at a hoster ask him to do these changes.

Cheers

Kai