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23 February, 15:53
Solve x^4-12x^2-64=0
+4
Answers (
2
)
Corinne Fuentes
23 February, 17:07
0
(x^2 + 4) (x^2 - 16)
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Jake Macdonald
23 February, 19:23
0
x
4
-
12
x
2
=
64
x
4
-
12
x
2
=
64
Move
64
64
to the left side of the equation by subtracting it from both sides.
x
4
-
12
x
2
-
64
=
0
x
4
-
12
x
2
-
64
=
0
Rewrite
x
4
x
4
as
(
x
2
)
2
(
x
2
)
2
.
(
x
2
)
2
-
12
x
2
-
64
=
0
(
x
2
)
2
-
12
x
2
-
64
=
0
Let
u
=
x
2
u
=
x
2
. Substitute
u
u
for all occurrences of
x
2
x
2
.
u
2
-
12
u
-
64
=
0
u
2
-
12
u
-
64
=
0
Factor
u
2
-
12
u
-
64
u
2
-
12
u
-
64
using the AC method.
Tap for fewer steps ...
Consider the form
x
2
+
b
x
+
c
x
2
+
b
x
+
c
. Find a pair of integers whose product is
c
c
and whose sum is
b
b
. In this case, whose product is
-
64
-
64
and whose sum is
-
12
-
12
.
-
16
,
4
-
16
,
4
Write the factored form using these integers.
(
u
-
16
)
(
u
+
4
)
=
0
(
u
-
16
)
(
u
+
4
)
=
0
Replace all occurrences of
u
u
with
x
2
x
2
.
(
x
2
-
16
)
(
x
2
+
4
)
=
0
(
x
2
-
16
)
(
x
2
+
4
)
=
0
Rewrite
16
16
as
4
2
4
2
.
(
x
2
-
4
2
)
(
x
2
+
4
)
=
0
(
x
2
-
4
2
)
(
x
2
+
4
)
=
0
Since both terms are perfect squares, factor using the difference of squares formula,
a
2
-
b
2
=
(
a
+
b
)
(
a
-
b
)
a
2
-
b
2
=
(
a
+
b
)
(
a
-
b
)
where
a
=
x
a
=
x
and
b
=
4
b
=
4
.
(
x
+
4
)
(
x
-
4
)
(
x
2
+
4
)
=
0
(
x
+
4
)
(
x
-
4
)
(
x
2
+
4
)
=
0
If any individual factor on the left side of the equation is equal to
0
0
, the entire expression will be equal to
0
0
.
x
+
4
=
0
x
+
4
=
0
x
-
4
=
0
x
-
4
=
0
x
2
+
4
=
0
x
2
+
4
=
0
Set the first factor equal to
0
0
and solve.
Tap for fewer steps ...
Set the first factor equal to
0
0
.
x
+
4
=
0
x
+
4
=
0
Subtract
4
4
from both sides of the equation.
x
=
-
4
x
=
-
4
Set the next factor equal to
0
0
and solve.
Tap for more steps ...
x
=
4
x
=
4
Set the next factor equal to
0
0
and solve.
Tap for more steps ...
x
=
2
i
,
-
2
i
x
=
2
i
,
-
2
i
The final solution is all the values that make
(
x
+
4
)
(
x
-
4
)
(
x
2
+
4
)
=
0
(
x
+
4
)
(
x
-
4
)
(
x
2
+
4
)
=
0
true.
x
=
-
4
,
4
,
2
i
,
-
2
i
x
=
-
4
,
4
,
2
i
,
-
2
i
x
4
-
1
2
x
2
=
6
4
x
4
-
1
2
x
2
=
6
4
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