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Byju's Answer
Standard X
Mathematics
Solving a Quadratic Equation by Completion of Squares Method
Solve the giv...
Question
Solve the given quadratic equation by completing the square,
x
2
−
3
x
+
1
=
0
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Solution
The given quadratic equation is
x
2
−
3
x
+
1
=
0
.
Add and subtract
9
4
in the equation
x
2
−
3
x
+
1
=
0
to make a perfect square as shown below:
x
2
−
3
x
+
1
=
0
⇒
x
2
−
3
x
+
9
4
−
9
4
+
1
=
0
⇒
(
x
)
2
−
(
2
×
x
×
3
2
)
+
(
3
2
)
2
+
(
−
9
4
+
1
)
=
0
⇒
(
x
−
3
2
)
2
−
5
4
=
0
(
∵
(
a
−
b
)
2
=
a
2
+
b
2
−
2
a
b
)
⇒
(
x
−
3
2
)
2
=
5
4
⇒
x
−
3
2
=
±
√
5
4
⇒
x
−
3
2
=
±
√
5
2
⇒
x
−
3
2
=
−
√
5
2
,
x
−
3
2
=
√
5
2
⇒
x
=
−
√
5
2
+
3
2
,
x
=
√
5
2
+
3
2
⇒
x
=
3
−
√
5
2
,
x
=
3
+
√
5
2
Hence,
x
=
3
−
√
5
2
or
x
=
3
+
√
5
2
.
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