Solve $x+e^{x}=2.$ Express the solution rounded to three decimal places.

Solution We can approximate the solution to the equation by graphing the two functions $Y_{1}=x+e^{x}$ and $Y_{2}=2.$ Then we use graphing technology to approximate the intersection of the graphs. Since the function $Y_{1}$ is increasing (do you know why?) and the function $Y_{2}$ is constant, there will be only one point of intersection. Figure 69 shows the graphs of the two functions and their intersection. They intersect when $x\approx 0.4428544$, so the solution of the equation is $0.443$ rounded to three decimal places.