Answer
\begin{align*}
\text{Discriminant: }&
0
\\\text{Number of Real Solutions: }&
1
\end{align*}
Work Step by Step
Using the properties of equality, the given equation, $
x^2+8x=-16
,$ is equivalent to
\begin{align*}
x^2+8x+16=0
.\end{align*}
In the equation above $a=
1
,$ $b=
8
,$ and $c=
16
.$
Using the Discriminant Formula which is given by $b^2-4ac,$ the value of the discriminant is
\begin{array}{l}\require{cancel}
&
8^2-4(1)(16)
\\&=
64-64
\\&=
0
\end{array}
Since the discriminant is equal to $0,$ then there is $1$ real solution. Hence,
\begin{align*}
\text{Discriminant: }&
0
\\\text{Number of Real Solutions: }&
1
\end{align*}
