Answer
Algebraically, we get $x=5\pm 2\sqrt[4]{5}$.
Graphically, we get $x=2.0093$ and $x=7.9907$.
Work Step by Step
Solve algebraically:
$(x-5)^4-80=0$ (Add with 80)
$(x-5)^4=80$ (Take the fourth root)
$x-5=\pm \sqrt[4]{80}$ (Add with 5)
$x=5\pm \sqrt[4]{80}$
$x=5\pm 2\sqrt[4]{5}$
Solve graphically:
We sketch the graph of $y=(x-5)^4-80$ as shown below.
In addition, the graph intercepts the x-axis at $x=2.0093$ and $x=7.9907$.
Then, the solutions are $x=2.0093$ and $x=7.9907$.
