There are two things you can try before buying weird hdmi to dvi cables (do those even exist?)
1. In system preferences > display settings > arrangement tab you can set your “main” display by dragging the white bar in the blue squares representing your monitor. First try making your non-hdmi monitor as the main one. Inside fcpx disable a/v output. Try showing events on your hdmi display.
2. If the above doesn’t work try in system preferences to set your hdmi display as your main display. Drag the main fcp window to your non hdmi screen. Try showing events on your hdmi display.
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