Answer
The solutions are $x=\left\{-2.782, -0.508, 0.508, 2.782\right\}$.
Work Step by Step
To solve the given equation graphically, perform the following steps:
(1) Graph the function $y=x^4-8x^2+2$ using a graphing utility. Refer to the image below for the graph.
(2) Identify the point/s where the graph touch/cross the x-axis. These are the points where the value of $x^4-8x^2+2$ is zero.
The x-coordinates of these points are the solutions to the given equation.
Notice that the graph crosses the x-axis at $(-2.782, 0), (-0.508,0), (0.508, 0)$ and $(2.782, 0)$.
This means that the solutions to the given equation are: $-2.782, -0.508, 0508$, and $2.782$.
Thus, the solutions are $x=\left\{-2.782, -0.508, 0.508, 2.782\right\}$.
