Posted by Anne on Thursday, December 8, 2011 at 12:50am.
2 x ^ 2 - 20 x - 3
2 ( x ^ 2 - 10 x - 3 / 2 )
2 ( x ^ 2 - 10 x + ? - 3 / 2 ) + ?
The quantity to add is "the square of: (1/2) times the coefficient of the middle term -10"
That is:
[ ( 1 / 2 ) * ( - 10 ) ] ^ 2
( - 5 ) ^ 2
2 ( x ^ 2 - 10 x - 3 / 2 )=
2 [ x ^ 2 - 10 x + ( - 5 ) ^ 2 - 3 / 2 ) - ( - 5 ) ^ 2 ]
2 [ x ^ 2 - 10 x + ( - 5 ) ^ 2 ] - 2 * 3 / 2 - 2 * 25
x ^ 2 - 10 x + ( - 5 ) ^ 2 = ( x - 5 ) ^ 2
2 * 3 / 2 = 3
2 * 25 = 50
2 [ x ^ 2 - 10 x + ( - 5 ) ^ 2 - 3 / 2 ) - ( - 5 ) ^ 2 ] =
2 ( x - 5 ) ^ 2 - 3 - 50 =
2 ( x - 5 ) ^ 2 - 53
2 x ^ 2 - 20 x - 3 = 2 ( x - 5 ) ^ 2 - 53
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