Answer
$2$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To evaluate the given summation expression, $
\displaystyle\sum_{i=1}^3 (x_i^2+x_i)
,$ substitute $
i
$ with the values from $
1
$ to $
3
.$ Then substitute the given values for each $x_i$'s
$\bf{\text{Solution Details:}}$
Substituting $
i
$ with the numbers from $
1
$ to $
3
,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
(x_1^2+x_1)+(x_2^2+x_2)+(x_3^2+x_3)
\\\\=
x_1^2+x_1+x_2^2+x_2+x_3^2+x_3
\\\\=
x_1^2+x_2^2+x_3^2+x_1+x_2+x_3
.\end{array}
Using the given values $x_1=-2,x_2=-1,$ and $x_3=0,$ the expression above evaluates to
\begin{array}{l}\require{cancel}
(-2)^2+(-1)^2+0^2+(-2)+(-1)+0
\\\\=
4+1+0-2-1+0
\\\\=
2
.\end{array}
