>> Then we have -340 K = 3,400 = 4.905 K^2, which I still don't know how to 
>> solve.
> 
>   That's not what you had. You had this:
> 
> -340 K + 3,400 = 4.905 K^2

Yeah, a simple typo.

> which is equivalent to
> 
> 4.905 K^2 + 340 K + 3400 = 0

Mmm, I hadn't realised that.

[But... are the signs correct?]

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