HP 33s - Manual (Page 118)

7–8 Solving Equations
„ If an equation does not allow certain values for the unknown, guesses can
prevent these values from occurring. For example,
y = t + log x
results in an error if x ≤ 0 (message !).
In the following example, the equation has more than one root, but guesses help
find the desired root.
Example: Using Guesses to Find a Root.
Using a rectangular piece of sheet metal 40 cm by 80 cm, form an open–top box
having a volume of 7500 cm
3
. You need to find the height of the box (that is, the
amount to be folded up along each of the four sides) that gives the specified
volume. A taller box is preferred to a shorter one.
40
80
40_2H
H
H
80_2H H H
If H is the height, then the length of the box is (80 – 2H) and the width is (40 – 2H).
The volume V is:
V = ( 80 – 2H ) × (40 – 2H ) × H
which you can simplify and enter as
V = ( 40 – H ) × ( 20 – H ) Ч 4 Ч H