Expert: Sherman D. - 9/30/2007

Question
i've tried to solve this equation by completing by square but couldn't find a conclusive answer. Can you show me please all steps when completing by square?
3x2-2x-6=0
PS: Could you please show me how to check the answer?
Thank you

Answer
3x^2 - 2x - 6 = 0
3x^2 - 2x = 6
x^2 - (2/3)x = 2
x^2 - (2/3)x + (1/9) = (19/9)
(x - (1/3))^2 = (19/9)
x - (1/3) = ±sqrt(19/9)
x - (1/3) = ±(1/3)sqrt(19)
x = (1/3) ± (1/3)sqrt(19) or (1/3)(1 ± sqrt(19))

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here's another way to do this, using the quadratic formula, which is the conclusion to completing the square.

x = (-b ± sqrt(b^2 - 4ac))/(2a)

x = (-(-2) ± sqrt((-2)^2 - 4(3)(-6)))/(2(3))
x = (2 ± sqrt(4 + 72))/6
x = (2 ± sqrt(76))/6
x = (2 ± sqrt(4 * 19))/6
x = (2 ± 2sqrt(19))/6
x = (1/3)(1 ± sqrt(19))