You should not have set a BIOS password if you were not even going to the trouble to write it down. It is VERY expensive to get HP to reset that.
Please note that now, to resolve a forgotten BIOS password issue, a system board replacement is required -- and additional customer costs apply, HP has issued this post about BIOS passwords: https://support.hp.com/us-en/document/c06368824.
4d. No posts shall include instructions or directions intended to bypass or subvert security measures, including passwords, locking mechanisms, fingerprint scans, etc., or to bypass any safety measures.
For assistance NOW, you have to contact your regional HP Customer Support location directly as they will confirm ownership of the PC before providing any assistance -- something we are not able to do from here.