fest
solid
Having a hard, stable consistency; not liquid or gaseous.
Der Boden ist nach dem Frost wieder fest.
After the frost, the ground is firm again.

firm / fixed
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solid
Having a hard, stable consistency; not liquid or gaseous.
Der Boden ist nach dem Frost wieder fest.
After the frost, the ground is firm again.

The adjective 'fest' is also very often used as an adverb to intensify a verb. It then means 'strongly', 'firmly', or 'intensely'.
Sie drückte seine Hand ganz fest.
She squeezed his hand very tightly.
Words like 'befestigen' (to attach/fasten something), 'festhalten' (to hold on to something/not let go), or 'die Festung' (a stable fortified building/fortress) belong to the same word family and share the basic idea of stability.
Kannst du bitte das Bild an der Wand befestigen?
Can you please attach the picture to the wall?
In the meaning 'stable' or 'sturdy', 'fest' is often combined with things that provide support, e.g. 'fester Boden' (firm ground), 'festes Schuhwerk' (sturdy footwear), or 'ein fester Händedruck' (a firm handshake).
Für die Wanderung brauchst du festes Schuhwerk.
You need sturdy footwear for the hike.
In social and professional life, 'fest' expresses a binding, lasting relationship. Typical combinations are 'eine feste Stelle' (a permanent position), 'ein fester Termin' (a fixed appointment), or 'ein fester Freund / eine feste Freundin' (a steady boyfriend/girlfriend).
Wir haben noch keinen festen Plan für das Wochenende.
We don't have a fixed plan for the weekend yet.
When 'fest' means 'with force', it often appears as an adverb with verbs like 'halten' (to hold), 'ziehen' (to pull), 'drücken' (to press/squeeze), or 'umarmen' (to hug).
Er umarmte seine Mutter ganz fest zum Abschied.
He hugged his mother very tightly when saying goodbye.
The combination 'fest schlafen' (to sleep soundly) is a fixed expression and means that someone sleeps very deeply and well.
Trotz des Lärms hat das Kind die ganze Zeit fest geschlafen.
Despite the noise, the child slept soundly the whole time.
To express a strong, unshakable opinion, 'fest' is used in fixed expressions like 'fest davon überzeugt sein' (to be firmly convinced of it), 'fest daran glauben' (to firmly believe in it), or 'fest damit rechnen' (to fully expect it).
Sie rechnet fest damit, die Prüfung zu bestehen.
She fully expects to pass the exam.
go / loose
'los' and 'fest' form a clear contrast when it comes to whether something is holding in place. Here, 'los' means that something is not properly attached or has come loose. 'fest' means that something sits stably, holds well, or is tightly connected. You use 'los' when a part wobbles or has come off. 'fest' fits when you want to say that something cannot easily be moved or loosened.

Nach der Reparatur sitzt das Regal wieder fest an der Wand.
After the repair, the shelf is firmly attached to the wall again.
Die Schraube am Stuhl ist los und muss angezogen werden.
The screw on the chair is loose and needs to be tightened.