Answer
Algebraically, we get $x=\frac{3}{2}\sqrt[5]{16}$.
Graphically, we get $x=2.6117$.
Work Step by Step
Solving algebraically:
$2x^5-243=0$ (Add with 243)
$2x^5=243$
$2x^5=3^5$
$x^5=\frac{3^5}{2}$
$x^5=\frac{3^5\cdot 16}{2^5}$ (Take the fifth root)
$x=\frac{3}{2}\sqrt[5]{16}$
Solve graphically:
We sketch the graphs of $y=2x^5-243$ as shown below.
The graph intercepts the x-axis at $x=2.6117$.
So, the solution is $x=2.6117$.
