What built in Functionality is Best to Solve this.

[ppal]

Given 

Soln x=1 and x=-1

I have tried the solve box - the answer depends on the seed value.

 Best approach to solve in Mathcad?  Thanks.

[Werner_E · Accepted solution]

A solve block in Prime only uses numerical approximation algorithms and will always give you just one solution which depends on the guess value, as you found out yourself.

The symbolic "solve" should give you all solutions, especially when you combine it with "fully". But the symbolic engine in Prime/Mathcad is to weak and not capable to do so - it yields just one of the two solutions:

You can plot the LHS and RHS of the equation to see that there are two solutions

You can also combine different guess values in a vector and so get both solutions in one go

Its no surprise that Wolfram Alpha does a much better job with this:

I guess that Mathcad 11 (with Maple under the hood) will do a better job, too.

[LucMeekes]

"I guess that Mathcad 11 (with Maple under the hood) will do a better job, too."

Don't set the expectation for that old version of Maple too high:

Why is the first answer not (just) 1 instead of 1.0000000?

There's no way to get a negative or complex result from the symbolic solver.

Luc

[Werner_E]

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@LucMeekes wrote:

"I guess that Mathcad 11 (with Maple under the hood) will do a better job, too."

Don't set the expectation for that old version of Maple too high:

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Well, it seems that sometimes we glorify the good old things a bit too much. 🤔

[ValeryOchkov]

[Werner_E]

Yes, the "root" function can be used, too. And you also can use multiple guesses in one go if you vectorize:

The root function in its variant with four arguments can also be evaluated symbolically, but like the symbolic "solve" it would yield just one of the many solutions and the range for x provided has no effect at all:

I found no way to talk Mathcad or Prime into giving a complete closed solution like