```PROGRAM Newton4;
{ From Borland Pascal Programs for Scientists and Engineers }
{ by Alan R. Miller, Copyright C 1993, SYBEX Inc }

USES WinCrt;  { Crt for non-windows version }
VAR
X, X2  : Real;
AllDone: Boolean;
Error  : Boolean;

PROCEDURE Func (X: Real; VAR Fx, Dfx: Real);
BEGIN
Fx := X * X - 2.0;
Dfx := 2.0 * X
END; { Func }

PROCEDURE Newton(VAR X: Real);

CONST
Tol   = 1.0E-6;
Max = 20;

VAR
Fx, Dfx, Dx, X1: Real;
I: Integer;

BEGIN  { Newton }
Error := False;
I := 0;
REPEAT
I := I + 1;
X1 := X;
Func(X, Fx, Dfx);
IF Dfx = 0.0 THEN
BEGIN
Error := True;
X := 1.0;
WriteLn('ERROR: slope zero')
END
ELSE
BEGIN
Dx := Fx / Dfx;
X := X1 - Dx;
WriteLn
('X= ',X1, ', Fx= ',Fx, ', Dfx= ',Dfx)
END
UNTIL
Error  OR
(I >= Max) OR
(Abs(Dx) <= Abs(Tol * X));
IF I >= Max THEN
BEGIN
WriteLn
('ERROR: no convergence in ',
Max, ' loops');
Error := True
END
END; { Newton }

BEGIN     { main program }
AllDone := False;
REPEAT
WriteLn; Write (' First guess: ');
IF X < -19.0 THEN AllDone := True
ELSE
BEGIN
Newton(X);
WriteLn;
IF NOT Error THEN
WriteLn('The solution is ', X:9:5);
WriteLn
END
UNTIL AllDone;
DoneWinCrt { for Windows version only }
END.

```