Obtained: Lieutenant Boyd in McCarran.
Speak with Lieutenant Boyd about missing soldiers on the base to get this quest (Picture 1). Start by going to the camp hall to find Corporal White's locker, inside you will find his diary and some research leads (Image 2-3).
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Now go to the Gomorrah and speak with Dazzle in the inner courtyard of the casino (Picture 4). The young lady will refer you to the NCR farmers outside of Vegas. Go to the farms and speak with Trent Bascom then with Lieutenant Romanowski (Picture 5-6).
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You have learned that Corporal White has made contact with a certain Anderson, so go to Westside to meet him (Picture 7-8). Anderson won't teach you much, unless you have enough intelligence, in which case you can immediately unmask him and move on to the last step described below (Image 9).
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If you can't unmask Anderson yet, go out into the street and talk to young Hector (Picture 10). This one will refuse to tell you where it finds its water, all you have to do is follow it during its day to learn more. Just advance the time a few hours and then enter the northern basin of Freeside to find the kid (Image 11). He will tell you that Anderson is responsible for White's disappearance (Picture 12).
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Go back to Anderson and make him confess (Picture 13), you can then kill him, have him arrested and keep his secret (better reputation with the disciples of the apocalypse) or even settle financially. Either way, return to Lieutenant Boyd to complete the quest and collect your reward. This will also give you the key to a box of confiscated material that you will find in the cells, in front of McCarran's interrogation room (Image 14).
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Alternative outcomes:
Eliminate Anderson
Trap the Scorpion Gang
Make a deal with Anderson (10% of co-op revenue)