HP -32S Owner's Manual page 272

It's apparent from inspecting the equation that if x is a negative num
ber, the smallest that /fa) can be is 10. /fa) approaches 10 as x becomes
a negative number of large magnitude.
Example: A Math Error. Find the root of the equation:
\j[x -f- (x + 0.3)] - 0.5
Enter the function as the program:
101 LBL I
102 RCL X
103 0.3
104 RCL+ X
105 -r
106 SQRT
107 0.5
108 -
109 RTN
First attempt to find a positive root.
Keys: Display:
•I SOLVE/J | {FN} I
orsToix 10
11 SOLVE/J | {SOLVE}
X X= 0.1000
0.
Description:
Calculates the root us
ing guesses 0 and 10.
Now attempt to find a negative root by entering guesses 0 and —10.
Notice that the function is undefined for values of x between 0 and
—0.3 since those values produce a positive denominator but a nega
tive numerator, causing a negative square root.
OfSTQlX 10 [J73
Bl SOLVE/J | {SOLVE}
X
Ml VIEW | X
SQRT(NEG)
X=-0.1308
270 C: More About Solving an Equation
Math error.
Displays the final esti
mate of x.