Breakdown of Wir haben zu Fuß gehen müssen, denn das Auto hat eine zusätzliche Reparatur gebraucht.
ein
a, an (eine)
haben
to have
das Auto
the car
wir
we
brauchen
to need
müssen
to have to, must
denn
because
zu Fuß gehen
to go on foot, to walk
die Reparatur
the repair
zusätzlich
additional / additionally
Questions & Answers about Wir haben zu Fuß gehen müssen, denn das Auto hat eine zusätzliche Reparatur gebraucht.
Why does the first part end with gehen müssen instead of a past participle like gemusst?
This is the double infinitive rule for the Perfekt tense. When a modal verb like müssen is used together with a main verb like gehen, we do not use the past participle gemusst. Instead, both verbs stay in their infinitive (dictionary) form and pile up at the end of the clause.
Since gehen involves motion, why do we use haben instead of sein as the helping verb (Wir haben...)?
You are right that gehen on its own takes sein in the Perfekt tense. However, in this sentence, the helping verb is determined by the modal verb müssen. Modal verbs always take haben in the Perfekt tense, regardless of which action verb they are paired with.
Both denn and weil mean "because." Why doesn't the verb hat go to the very end of the sentence after denn?
The word denn is a coordinating conjunction, meaning it simply links two normal sentences without changing their word order. It acts as a bridge in "position 0," so the subject das Auto is position 1 and the verb hat stays in its normal position 2. If the sentence had used weil, the verb would indeed be pushed to the end: ...weil das Auto eine zusätzliche Reparatur gebraucht hat.
Why does the adjective zusätzliche end in -e here?
The phrase eine zusätzliche Reparatur is the direct object being needed, so it is in the accusative case. Because Reparatur is a feminine noun, the adjective after the indefinite article eine takes the standard feminine accusative ending, which is -e.
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