It's been brought up a couple times, but just to be sure nobody glosses over it, I'll say it once more extra loud.
YOU CAN'T TAKE AGONIZING BLAST WITH ELDRITCH ADAPT
...unless you are already a Warlock. The feat doesn't allow non-Warlocks to take invocations that have requirements even if they meet the requirements.
Edit: Here's an additional note to save some people some book searching: Every invocation in XGtE has a requirement.
Here is the list of invocations non-warlocks can take with the feat. It's sort of a mini-guide. I am curious about the ones which do not list a prerequisite but mention "using a warlock spell slot" and how that works with the feat for a non-warlock.
Armor of Shadows: You can cast
mage armor on yourself at will, without expending a spell slot or material components.
Beast, Speech: You can cast
speak with animals at will, without expending a spell slot.
Beguiling Influence: You gain proficiency in the
Deception and
Persuasion skills.
Devil's Sight: You can see normally in darkness, both magical and nonmagical, to a distance of 120 feet.
Eldritch Sight: You can cast
detect magic at will, without expending a spell slot.
Eyes of the Rune Keeper: You can read all writing.
Fiendish Vigor: You can cast
false life on yourself at will as a 1st-level spell, without expending a spell slot or material components.
Gaze of Two Minds: You can use your action to touch a willing humanoid and perceive through its senses until the end of your next turn. As long as the creature is on the same plane of existence as you, you can use your action on subsequent turns to maintain this connection, extending the duration until the end of your next turn. While perceiving through the other creature’s senses, you benefit from any special senses possessed by that creature, and you are
blinded and
deafened to your own surroundings.
Mask of Many Faces: You can cast
disguise self at will, without expending a spell slot.
Misty Visions: You can cast
silent image at will, without expending a spell slot or material components.
Thief of Five Fates: You can cast
bane once using a warlock spell slot. You can’t do so again until you finish a long rest.
There are some great invocations in there. But yeah, not Agonizing Blast.