#### Answer

$x=-1$

#### Work Step by Step

We can write the given equation as:
$(x^{1/3})^2+2x^{1/3} +1=0$
Let
$u=x^{1.3}$
Then
$u^2= (x^{1/3})^2$
Rewrite the given equation using the variable $u$ to obtain:
$u^2+2u+1=0$
Factor the trinomial to obtain:
$(u+1)(u+1)=0$
Use the Zero-Factor Property by equating each unique factor to zero. then solve:
$u+1 = 0
\\u=-1$
Since $u=x^{1/3}$, then
$u= -1
\\x^{1/3}=-1
\\(x^{1/3})^3=(-1)^3
\\x=-1$
Thus, the solution is $x=-1$.