to pay for
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to pay for something
To have to bear the negative consequences of something that another person caused or did wrong.
Sein Kollege hat den Fehler gemacht, aber er musste die Sache beim Chef ausbaden.
His colleague made the mistake, but he had to pay for it with the boss.
'Ausbaden' (to pay for something) is a separable verb. The prefix 'aus-' goes at the end in a main clause. In subordinate clauses or in the infinitive with 'zu', the verb stays together.
Mein Kollege war krank, also musste ich seine Arbeit mit ausbaden.
My colleague was sick, so I had to help pay for his work too.
The word is made up of 'aus-' and 'baden' (to bathe). The meaning is purely figurative and should not be understood literally. You bear the unpleasant consequences of an action, as if you proverbially had to 'bathe' in something unpleasant.
Der Praktikant hat den Kaffee verschüttet, und ich durfte es vor dem Kunden ausbaden.
The intern spilled the coffee, and I was the one who had to pay for it in front of the customer.
The expression 'etwas ausbaden' (to pay for something) belongs to colloquial language. It describes in a very vivid and slightly informal way how someone has to bear the consequences for others.
Jetzt darf ich den ganzen Schlamassel allein ausbaden, toll!
Now I get to pay for the whole mess by myself, great!
to bathe / swim
'baden' and 'ausbaden' look very similar, but usually they do not mean the same thing. 'baden' is used literally when someone is in water, for example in the bathtub, in a lake, or in the sea. 'ausbaden' does not mean that you bathe for longer; it means that you have to bear the negative consequences of something. What can be confusing is that there is also the fixed expression 'etwas ausbaden müssen' (to have to pay for something). Without 'aus-', it is usually about water; with 'aus-', it is about unpleasant consequences.
Die Gäste kamen zu spät, und der Kellner musste den Ärger ausbaden.
The guests arrived late, and the waiter had to deal with the trouble.
Im Sommer baden die Kinder gern im See hinter dem Campingplatz.
In summer, the children like swimming in the lake behind the campsite.