None of the SQL Server Editions that support Web Clients are free. HP may have a licensing agreement with Microsoft, since according to
http://bizsupport1.austin.hp.com/bc/.../c01857435.pdf the distributions from HP include the Microsoft SQL Server Express Edition.
Based on the PDF I cited above that is provided by HP, as an end user you should not need to install or configure anything. The HP distribution ought to take care of everything for you when it installs the software.
-PatP