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Solving an Equation

A common mathematical problem involves finding the solution to an equation. For example, to determine the solution to the equation tex2html_wrap_inline1183 , make sure that your calculator is in radian mode, then push the following keys: 2pt tex2html_wrap609 tex2html_wrap1207 . This opens the solve menu. The Solve equation option should be highlighted. Push tex2html_wrap1075 . The equation field should be highlighted. Enter either tex2html_wrap_inline1187 or tex2html_wrap_inline1183 . Without the equals sign the HP48G/GX will set the expression equal to zero, and then solve for the variable. Notice that the variable x now has its own field. Enter a guess for the value of the solution in the X field. After doing so, be sure to highlight the field X, which is the variable whose value we seek. Now push tex2html_wrap1207 . The number tex2html_wrap_inline1193 is displayed in the variable field. If we return to the standard screen tex2html_wrap_inline1195 , we see that this value has been tagged as x, and placed on the stack were it is available for use in another calculation.

We may also use this program to numerically solve a single equation in more than one unknown for one of the unknowns. For example lets solve the equation tex2html_wrap_inline1199 . The HP48G/GX cannot solve for x as a function of y, but if we specify a particular y value, it can solve for the corresponding x value. Try this for y=2. There are three solutions. Which one the HP48G/GX calculates is determined by your initial guess. Try x = 0.2, 0.7, and -2.0. Be sure to highlight the X field before you push solve.

We determined that there were three solutions by plotting the function tex2html_wrap_inline1203 . From the graph we determined approximate locations of the zeros of the function.

Mike Stecher
Thu Mar 21 09:53:31 CST 1996