Answer:Since both terms are perfect cubes, factor using the difference of cubes formula,
a
3
−
b
3
=
(
a
−
b
)
(
a
2
+
a
b
+
b
2
)
where
a
=
x
and
b
=
2
.
(
x
−
2
)
(
x
2
+
x
⋅
2
+
2
2
)
=
0
Simplify.
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(
x
−
2
)
(
x
2
+
2
x
+
4
)
=
0
If any individual factor on the left side of the equation is equal to
0
, the entire expression will be equal to
0
.
x
−
2
=
0
x
2
+
2
x
+
4
=
0
Set the first factor equal to
0
and solve.
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x
=
2
Set the next factor equal to
0
and solve.
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x
=
−
1
+
i
√
3
,
−
1
−
i
√
3
The final solution is all the values that make
(
x
−
2
)
(
x
2
+
2
x
+
4
)
=
0
true.
x
=
2
,
−
1
+
i
√
3
,
−
1
−
i
√
3
Step-by-step explanation:
