Answer
Solving algebraically and graphically, we get the solution $x=\pm 2.5$.
Work Step by Step
Solve algebraically:
$16x^4=625$ (Substract with 625)
$16x^4-625=0$ (Factorize)
$(4x^2-25)(4x^2+25)=0$ (Note that $4x^2+25>0$)
$4x^2-25=0$ (Factorize)
$(2x+5)(2x-5)=0$
$x=-\frac{5}{2}$ or $x=\frac{5}{2}$
$x=-2.5$ or $x=2.5$
Solve graphically:
We sketch the graphs of $y_1=16x^4$ and $y_2=625$ as shown below.
Both intersect at $x=-2.5$ and $x=2.5$.
So, the solution is $x=\pm 2.5$.
