HP -22S Owner's Manual page 170

Round-Off Error and Underflow
Round-Off Error. The limited (12-digit) precision of the calculator
can cause Mround-off' errors that adversely affect iterative solutions.
For example:
has no roots because the left side of the equation is always positive.
However,
I
SOLVE
I
returns the answer 2.0000 for initial guesses of 1
and 2, due to round-off.
Round-off can also cause
I
SOLVE
I
to fail to find a root. The equation:
ABS(X2 - 7)
=
0
has a root at
V7.
However, no 12-digit number
exactly
equals
V7,
so
the function never equals O. Furthermore, the function never changes
sign.
I
SOLVE
I
returns the message
HO ROOT FHD.
Underflow. Underflow can also affect
I
SOLVE
I
results. For example, con-
sider the equation:
whose root is infinite in value. Because of underflow,
I
SOLVE
I
returns a
very large value as a root.
170 B: More About Solving Equations