# Chapter 1, Equations and Graphs - Section 1.9 - Solving Equations and Inequalities Graphically - 1.9 Exercises: 22

The solutions are $x=\left\{0, 2.32\right\}$.

#### Work Step by Step

To solve the given equation graphically, perform the following steps: (1) Graph the functions $y=1+\sqrt{x}$ and $y=\sqrt{1+x^2}$. Refer to the image below for the graph. (2) Identify the point/s where the graphs intersect each other.. These are the points where the values of $1+\sqrt{x}$ and $\sqrt{1+x^2}$ are equal to each other.. The x-coordinates of these points are the solutions to the given equation. Notice that the graphs intersect each other at $(2.315, 2.521)$ and $(0, 1)$. This means that the solution to the given equation are $0$ and $\approx 2.32$. Thus, the solutions are $x=\left\{0, 2.32\right\}$.

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