Posted by gagan on Thursday, March 26, 2009 at 8:37pm.
step1
always factor out the coefficient of the x^2 term, unless it is already 1
this guarantees that it will be just x^2
-2x^2+3x-1
= -2[x^2 - 3/2 + ...] - 1
now take 1/2 of the coefficient of the x term, square that result, and then add and subtract it
1/2 of -3/2 is -3/4, which when squared is 9/16
= -2[x^2 - 3/2 + 9/16 - 9/16] - 1
your first 3 terms inside the bracket are your "perfect square"
= -2[x - 3/4)^2 - 9/16] - 1
now multiply through by the -2
= -2(x - 3/4)^2 + 9/8 - 1
simplify the end part
= -2(x - 3/4)^2 + 9/8 - 8/8
= -2(x - 3/4)^2 + 1/8
the middle term should of course be (-3/2)x in two of the above lines.
I am pretty sure you know where the typo error is.
r u there gagan
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