Answer:
8
Step-by-step explanation:
Find two factors of
16
which differ by
6
. The pair
8
,
2
works in that
8
×
2
=
16
and
8
−
2
=
6
.
Hence we find:
0
=
x
2
+
6
x
−
16
=
(
x
+
8
)
(
x
−
2
)
So
x
=
2
or
x
=
−
8
Alternatively, complete the square then use the difference of squares identity:
a
2
−
b
2
=
(
a
−
b
)
(
a
+
b
)
with
a
=
(
x
+
3
)
and
b
=
5
as follows:
0
=
x
2
+
6
x
−
16
=
(
x
+
3
)
2
−
9
−
16
=
(
x
+
3
)
2
−
25
=
(
x
+
3
)
2
−
5
2
=
(
(
x
+
3
)
−
5
)
(
(
x
+
3
)
+
5
)
=
(
x
−
2
)
(
x
+
8
)
Hence zeros
x
=
2
and
x
=
−
8
