HP 35s Scientific Calculator - Manual (Page 129)

Solving Equations 7-7
Understanding and Controlling SOLVE
SOLVE first attempts to solve the equation directly for the unknown variable. If the
attempt fails, SOLVE changes to an iterative (repetitive) procedure. The procedure
starts by evaluating the equation using two initial guesses for the unknown variable.
Based on the results with those two guesses, SOLVE generates another, better guess.
Through successive iterations, SOLVE finds a value for the unknown that makes the
value of the equation equal to zero.
When SOLVE evaluates an equation, it does it the same way  does — any
"=" in the equation is treated as a " – ". For example, the Ideal Gas Law equation
is evaluated as P
× V – (N × R × T). This ensures that an equality or assignment
equation balances at the root, and that an expression equation equals zero at the
root.
Some equations are more difficult to solve than others. In some cases, you need to
enter initial guesses in order to find a solution. (See "Choosing Initial Guesses for
SOLVE," below.) If SOLVE is unable to find a solution, the calculator displays
  .
See appendix D for more information about how SOLVE works.
Verifying the Result
After the SOLVE calculation ends, you can verify that the result is indeed a solution
of the equation by reviewing the values left in the stack:
The X–register (press  to clear the viewed variable) contains the solution
(root) for the unknown; that is, the value that makes the evaluation of the
equation equal to zero.
 
value Stores 4 in E ;prompts for F.
 

Stores 11 in F and
calculates x and y.
Ø 

value of y