# Chapter 1, Equations and Graphs - Section 1.9 - Solving Equations and Inequalities Graphically - 1.9 Exercises: 30

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 $x=\left\{-2.782, -0.508, 0.508, 2.782\right\}$.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.