to burst out: to depart quickly (also: to storm out); to act suddenly
For the second definition, this idiom is usually followed by a gerund form such as laughing, crying, singing, etc.
to make sense: to be sensible or reasonable
to cheer up: to make happier, to feel less sad (S)
to believe in: to accept as true, have faith in
to drop out of: to stop attending; to withdraw from
This idiom can be made into the noun form dropout.
to draw up: to prepare documents or legal papers(S)
to set out to: to intend to, to act purposefully to
to set out: to start traveling toward a place(also: to set off, to head out); to arrange or display neatly (also: to lay out) (S)
to run into: to meet someone unexpectedly; to crash or collide into (also: to bump into)