Note that we can assume all of $x_1,x_2,...,x_n$ to be non-negative real numbers. For each $i\in \{ 1,2,...,n\}$, if $x_i\geq \frac{1}{2}$, let $y_i=2x_i-1\geq 0$ and $z_i=1$. Otherwise, let $y_i=0$ and $z_i=2x_i\in [0,1)$. This gives us $|z_i|\leq 1$ for all $i\in \{ 1,2,...,n\}$. And $\sum_{i=1}^{n}{|y_i|}=\sum_{i=1}^{n}{y_i}=0+ \sum_{i\in A}{(2x_i-1)}\leq \sum_{i\in A}{x_i^2}\leq 1$ where $A=\{ i\in \{ 1,2,...,n\} \mid x_i\geq \frac{1}{2}\}$.