3002_60720
3 x square - 6 X + 2 is equal to zero
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Step 1 - Factor out the quadratic coefficient, thus:
3
x
2
+
6
x
−
2
=
3
{
x
2
+
2
x
−
2
3
}
Step 2 - Factor
1
2
of the
x
coefficient to form a perfect square, and subtract its square, and simplifiy, thus:
3
x
2
+
6
x
−
2
=
3
{
(
x
+
2
2
)
2
−
(
2
2
)
2
−
2
3
}
=
3
{
(
x
+
1
)
2
−
1
−
2
3
}
=
3
{
(
x
+
1
)
2
−
5
3
}
So now returning to the quadratic equation , we have;
3
x
2
+
6
x
−
2
=
0
∴
3
{
(
x
+
1
)
2
−
5
3
}
=
0
∴
(
x
+
1
)
2
−
5
3
=
0
∴
(
x
+
1
)
2
=
5
3
∴
x
+
1
=
±
√
5
3
∴
x
=
−
1
±
√
5
3
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