HP 35S EQN solve only finding one solution

[Trond]

Is anyone else having this problem?
Try a simple equation with two possible solutions for X, e.g. X^2-4=0.
My 35S seems to only be able to find one solution (2), while my 32SII finds either 2 or -2, depending on my starting values. I do this exactly the same for both; if I store negative values for x and in the x register, then 32SII finds the negative solution of -2, while positive gives 2. But 35S finds only 2, seemingly no matter what I do.

[Dieter]

(09-25-2017 08:56 PM)Trond Wrote:  Is anyone else having this problem?
Try a simple equation with two possible solutions for X, e.g. X^2-4=0.
My 35S seems to only be able to find one solution (2), while my 32SII finds either 2 or -2, depending on my starting values. I do this exactly the same for both; if I store negative values for x and in the x register, then 32SII finds the negative solution of -2, while positive gives 2. But 35S finds only 2, seemingly no matter what I do.

Yes, the 35s is far more intelligent than the 32SII in this regard. Since X only occurs once in the equation it can provide a symbolic (!) solution: x²–4 = 0 => x = √4 which is +2 for the 35s. Just the same as if you had pressed 4 √x.

That's why a solution is returned immediately, regardless of the two initial guesses in the variable X and the stack's x-register.

Of course you can also solve without this feature: simply add another X somewhere, e.g. by a simple X^2 + 0xX – 4. The "=0" part is not required. Now 0 STO X –5 SOLVE X returns -2. You will also notice that it takes a short moment before the solution is displayed. Just because now the result is not calculated directly but – as usual – approximated by iteration.

Dieter

[Trond]

Ah, I was wondering if it was doing that, because entering initial guesses that were far off from the solution did not make it take any longer to solve it. Thanks!

[Gene]

I think the 35S solver goes for the "direct" solution if there is one, i.e., square root (4) = +2.

If the equation is more complicated such as how Dieter suggests :-) then it is forced to avoid the quick, direct solution.

[Trond]

That does seem to be the case. I tried adding "+0xX" and that made the calculator start searching out different solutions, just like the 32SII.

I'm sure they had a reason to add this solution to the 35S, but I find it a bit counter-intuitive. Maybe to avoid the search getting stuck if there is an obvious solution? Still, I like my 35S, so it's good that I found out why it behaves like this.

[Logan]

Good to know