3x2-4x+1=0 by perfect square method
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Answer:
Solve by Completing the Square 3x^2-4x-1=0
3
x
2
−
4
x
−
1
=
0
Add
1
to both sides of the equation.
3
x
2
−
4
x
=
1
Divide each term by
3
and simplify.
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x
2
−
4
x
3
=
1
3
To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of
b
.
(
b
2
)
2
=
(
−
2
3
)
2
Add the term to each side of the equation.
x
2
−
4
x
3
+
(
−
2
3
)
2
=
1
3
+
(
−
2
3
)
2
Simplify the equation.
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x
2
−
4
x
3
+
4
9
=
7
9
Factor the perfect trinomial square into
(
x
−
2
3
)
2
.
(
x
−
2
3
)
2
=
7
9
Solve the equation for
x
.
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x
=
±
√
7
3
+
2
3
The result can be shown in multiple forms.
Exact Form:
x
=
±
√
7
3
+
2
3
Decimal Form:
x
=
1.54858377
…
,
−
0.21525043
…
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