solve by factorization method 2xsquare-9x-5=0
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Answered by
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Step-by-step explanation:
The solutions are
x
=
−
1
2
,
x
=
5
Explanation:
2
x
2
−
9
x
−
5
=
0
We can Split the Middle Term of this expression to factorise it and thereby find the 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
=
2
⋅
−
5
=
−
10
AND
N
1
+
N
2
=
b
=
−
9
After trying out a few numbers we get
N
1
=
−
10
and
N
2
=
1
−
10
⋅
1
=
−
10
, and
1
+
(
−
10
)
=
−
9
2
x
2
−
9
x
−
5
=
2
x
2
−
10
x
+
1
x
−
5
=
2
x
(
x
−
5
)
+
1
(
x
−
5
)
(
2
x
+
1
)
(
x
−
5
)
is the factorised form of the expression.
We now equate the factors to zero to obtain the solutions:
2
x
+
1
=
0
,
x
=
−
1
2
x
−
5
=
0
,
x
=
5
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