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```I'm new in this forum and I have a problem on my 35S:
when I try to solve for the expression x^2-4 I always find only the
positive root (2) even if I give it two initial estimates like -3
and -1 very close to the negative root (-2).
This happens only trying to solve the expression directly from the
EQN list, if I define the expression  in a program and I solve it
giving the same initial estimates, solve result is fine.
This is my operation sequence in RPN mode:
I insert the expression in the EQN list:
[EQN] X^2-4 [ENTER] [C]
I store in the X variable the first estimate (-3)
3[+/-][STO][X][ENTER]
I store in the X register the second estimate (-1)
1[+/-][ENTER]
from EQN list I recall the expression and I solve it for the variable X:
result is always 2
Could anyone explain me where I wrong ?
Thanks in advance and my best wishes for an happy 2012 to everybody.

```

Alessandro, there's nothing wrong with your 35s. You just discovered a feature that is often overlooked: the 35s can solve equations symbolically. It does so if the variable appears only once in the equation.

This also happens in your case. Here, the equation

``` X^2 - 4
```
or
``` X^2 - 4 = 0
```
is automatically transformed to
``` X = SQRT(4)
```
This exact solution is then evaluated by the 35s, using its regular functions. So the square root always returns a positive result.

This also means that - in such a case - the two initial guesses do not matter at all, they are completely ignored.

If you want the usual numerical solution by successive iteration, simply change the equation a bit so that the variable appears twice:

``` X*X - 4
```
or
``` X^2 - 4 = 0*X
```

Dieter

Edited: 31 Dec 2011, 11:18 a.m.

Thank you very much Dieter.

Alessandro

How fares the 35S with X! = 6 ??

Variable appearing exactly once but there is no inverse gamma function on the device that I'm aware of.

- Pauli

Without using the multiple variable trick in the equation it went for about 40 seconds and I canceled it.

Using the equation
X!=6+0*X

It returned 3.000 (my setting Fix 3) after about 10 seconds.

Well, there are some restrictions so that not all cases with a single appearance of the variable are solved symbolically. For instance, consider periodic functions like sin or cos. An equation like

```   SIN(X) = 0,5
```
will not be solved directly since there is an infinite number of solutions (30, 150, 390, 510, ... degrees). So the 35s will not simply set x = arcsin(0,5) and return 30 degrees.

The case you mentioned

```   X! = 6
```
cannot be solved directly since there is no inverse factorial or inverse Gamma function on the 35s. So the usual iterative approach is applied here. I tried various initial guesses between 0 and 20 - the 35s always came up with the correct result x = 3, usually within 4 - 10 seconds. No tweaking (...+0*X) was required.

Dieter