The solutions are
x
=
−
3
x
=
9
Explanation:
x
2
−
6
x
−
27
=
0
We can Split the Middle Term of this expression to factorise it and thereby find solutions.
In this technique, if we have to factorise an expression like
a
x
2
+
b
x
+
c
, we need to think of 2 numbers such that:
N
1
⋅
N
2
=
a
⋅
c
=
1
⋅
−
27
=
−
27
and
N
1
+
N
2
=
b
=
−
6
After trying out a few numbers we get
N
1
=
−
9
and
N
2
=
3
−
9
⋅
3
=
−
27
, and
3
+
(
−
9
)
=
−
6
x
2
−
6
x
−
27
=
x
2
−
9
x
+
3
x
−
27
x
2
−
9
x
+
3
x
−
27
=
0
x
(
x
−
9
)
+
3
(
x
−
9
)
=
0
(
x
+
3
)
(
x
−
9
)
=
0
is the factorised form of the expression.
Now we equate these factors to the R.H.S (
0
)
x
+
3
=
0
,
x
=
−
3
x
−
9
=
0
,
x
=
9
