Answer
$x\approx 1.755$
Work Step by Step
Rewrite as $f(x)=0$
$x(x-1)^{2}-1=0$
Note that
$f(1)=1(0)-1=-1$
$f(2)=2(1)-1=+1$
Since the function is a polynomial, it is continuous everywhere.
$y_{0}=0$ is a value between $f(1)$ and $f(2)$.
The Intermediate Value theorem guarantees that there exists a $c\in(1,2)$ for which $f(c)=0$.
Graphing, we find that the root is (approximately):
$x\approx 1.755$
