Solve the Quadratic equation by completing the square method . x square - 3x + 1 = 0
Answers
Answer:
The roots are
x
1
=
−
3
+
√
5
2
and
x
1
=
−
3
−
√
5
2
Explanation:
From the given
x
2
+
3
x
+
1
=
0
, we can see that the coefficient of x^2 is already 1, so we can begin with the coefficient of x which is 3.
The 3 will have to be divided by 2 then the result should be squared and the final result is
9
4
. This number will be added and subtracted in the equation on one side.
x
2
+
3
x
+
1
=
0
x
2
+
3
x
+
9
4
−
9
4
+
1
=
0
The first 3 terms now will form a PST-perfect square trinomial.
x
2
+
3
x
+
9
4
−
9
4
+
1
=
0
(
x
2
+
3
x
+
9
4
)
−
9
4
+
1
=
0
this
(
x
2
+
3
x
+
9
4
)
is equivalent to
(
x
+
3
2
)
2
So, the equation becomes
(
x
+
3
2
)
2
−
9
4
+
1
=
0
simplify
(
x
+
3
2
)
2
−
5
4
=
0
transpose the 5/4 to the right side
(
x
+
3
2
)
2
=
5
4
Extract the square root of both sides of the equation
√
(
x
+
3
2
)
2
=
√
5
4
x
+
3
2
=
±
√
5
2
x
=
−
3
2
±
√
5
2
The roots are
x
1
=
−
3
+
√
5
2
and
x
1
=
−
3
−
√
5
2
God bless....I hope the explanation is useful