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Solving Equations Graphically

Almost any equation in one variable can be solved graphically. The strategy is as follows: graph the left hand side and the right hand side of the equation on the same coordinate axes, and then trace the graph to find the point(s) where the two curves intersect. If there is no point of intersection then we say that the equation has no solution. The following example will illustrate this procedure.


Find all solutions of the equation . Round your answers to three decimal places.


First we will use the Plot-Solve tool to graph the left-hand side of the equation, and the right-hand side,  on the same coordinate axes. See Figure 1.

                                    Figure 1

The graph shows that there are two points of intersection. Click on one of the points and zoom in to find the coordinates of that point of intersection. Figure 2 shows that the intersection point on the left has coordinates (-3.3, 60).

                                    Figure 2

We can repeat the process to find the right intersection point. The coordinates are

(45.2, 60). See Figure 3.

                                    Figure 3

The equation has two solutions,  (accurate to one decimal place.