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August 21st, 2007, 02:20 PM   #1
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Complete the Square

When I complete the square of 3x^2 - 4x + 2 = 0, I get a totally different answer than when solving it using the quadratic formula.

Can anyone here solve this using completing the square and show me step by step?

The answer is:

x = (2 + sqrt{2}i)/3

and

x = (2 - sqrt{2}i)/3

Also, does it matter if I place the i before the square root symbol or after? In other words, should it be (sqrt{2}i) or i(sqrt{2}) for the question above?
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August 21st, 2007, 05:34 PM   #2
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Re: Complete the Square

0=3x^2-4x+2
0=x^2-(4/3)x+(2/3)
0=(x-(2/3))^2+(2/9)
(-2/9)=(x-(2/3))^2
?(-2/9)=x-(2/3)
?(-2/9)+(2/3)=x
Therefore, we get.. x=(2?(2)i)/3. You always put the number before an variable.
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