• The only functions in
which
the
unknown
variable
appears
are
ALOG,
EXP,
EXPM1, LN, LNP1, LOG,
and
SQRT.
•
The
only operators involving
the
unknown
variable are
+,
-,
x,
--;-,
and
A .
If
you are solving for a variable raised to a positive, even
power
(for example, A A 2 = 4), there
may
be
more
than
one
solu-
tion. However, if
the
solver
can
isolate
the
variable, it will find
one
of
the
solutions using
the
positive root. For example,
the
solver re-
arranges
W'
2=4
to A =
v'4
and
calculates
the
answer
+2.*
• The
unknown
variable does
not
appear
as
an
exponent.
Numerical Solutions
If
the
solver is
not
able to isolate
the
unknown
variable, it
cannot
provide a direct solution. In
these
cases,
the
solver searches for a
nu-
merical
solution.t
In its search for a numerical solution,
the
solver is looking for a value
that
sets
the
left-hand
side
of
the
formula
equal
to
the
right-hand
side.
To
do
this,
the
solver first uses two initial estimates
of
the
an-
swer,
which
we'll call estimate
#1
and
estimate
#2.
Using estimate
#1,
the
solver calculates values for
the
left
and
right side
of
the
for-
mula
(LEFT
and
RIGHT)
and
calculates LEFT
minus
RIGHT
(LEFT - RIGHT). Then,
the
solver does
the
same
calculations for esti-
mate
#2
.
If
neither
estimate
produces
a value
of
0 for LEFT - RIGHT,
the
solver analyzes
the
results
of
its calculations
and
produces
two
new
estimates
that
it judges to
be
closer to
the
answer.
By
repeating
this process
many
times,
the
solver
narrows
in
on
the
answer.
During
the
search for a numerical solution,
the
HP-18C
displays
the
two cur-
rent
estimates
and
the
sign
of
LEFT - RIGHT for
each
estimate (see
figure B-1).
• A formula
can
be
rewritten
to cause
the
solver to find
the
negative root. For example, if
A A 2 = 4
is
rewritten
as
(-
A)
2 =
4,
the
solver rearranges
the
formula to A = - v' 4
and
calculates
the
solution -
2.
t The solver's ability to find a numerical solution can often be
enhanced
by rewriting
the
formula so
that
the
unknown
variable
does
not
appear
as a divisor. For example,
the
solver
may
more
easily solve for A if
the
formula 1.;.
(AA2-A)
=B is
rewritten
as
(A
A
2-A)
xB=
1.
B:
More
About
HP·18C
Calculations
173
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