Answer
The solution is $x=\left\{1.62\right\}$.
Work Step by Step
To solve the given equation graphically, perform the following steps:
(1) Graph the function $y=x-\sqrt{x+1}$. Refer to the image below for the graph.
(2) Identify the point/s where the graph crosses/touches the x-axis. These are the points where the value of $x-\sqrt{x+1}$ is equal zero.
The x-coordinates of these points are the solutions to the given equation.
Notice that the graph crosses the x-axis at $(1.618, 0)$.
This means that the solution to the given equation is $\approx 1.62$.
Thus, the solution is $x=\left\{1.62\right\}$.
