[Q] Root with out unlocking the bootloader first/

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I wish the search worked better but I couldn't find this anywhere.

I'd like to know if I can first root the phone to install and use Titanium Backup. Then wipe the phone when I unlock the boot loader.

I was dumb and used the phone for 2+ weeks even though I KNEW I was going to eventually start using custom ROMs.

Simple answer is 'It's impossible'

Simple answer is all I wanted.

Thanks and damn it.