5x^2-3x-2=0 complete the square
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Answers
Answer:
Answer
Given 3x
2
−5x+2=0
Here, the coefficient of x
2
is 3 and it is not a perfect square.
∴ Multiply the equation throughout by 3.
⇒(3x
2
−5x+2=0)×3∴9x
2
−15x+6=0
Now, half of the coefficient of x is
2
5
.∴b=
2
5
and b
2
=(
2
5
)
2
So, 9x
2
−15x+(
2
5
)
2
−(
2
5
)
2
+6=0,(3x)
2
−15x+(
2
5
)
2
=(
2
5
)
2
−6
(3x−
2
5
)
2
=
4
25
−6=
4
1
(Taking square root on both the sides)
∴3x−
2
5
=±
2
1
∴3x−
2
5
=±
2
1
or 3x−
2
5
=−
2
1
3x=
2
1
+
2
5
3x=
2
5
−
2
1
Answer
Given 3x
2
−5x+2=0
Here, the coefficient of x
2
is 3 and it is not a perfect square.
∴ Multiply the equation throughout by 3.
⇒(3x
2
−5x+2=0)×3∴9x
2
−15x+6=0
Now, half of the coefficient of x is
2
5
.∴b=
2
5
and b
2
=(
2
5
)
2
So, 9x
2
−15x+(
2
5
)
2
−(
2
5
)
2
+6=0,(3x)
2
−15x+(
2
5
)
2
=(
2
5
)
2
−6
(3x−
2
5
)
2
=
4
25
−6=
4
1
(Taking square root on both the sides)
∴3x−
2
5
=±
2
1
∴3x−
2
5
=±
2
1
or 3x−
2
5
=−
2
1
3x=
2
1
+
2
5
3x=
2
5
−
2
1
3x=
2
6
=3 3x=
2
4
=2
∴x=1 x=
3x=
2
6
=3 3x=
2
4
=2
∴x=1 x=
Step-by-step explanation: