I think you have two options: Send it back to HP again, and tell them it's still not working, or buy a new one.
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Edit: I think I may have figured out the issue. If you have an Android phone, then Chrome OS pairs to it using a new feature, "Pair with Android phone", under Connected Devices, not Bluetooth.
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My Chromebook is managed by an organization, so I can't confirm if this works, but I definitely can show you where the setting is. [image|2663853]