To complete square one is basically doing a 2 + 2 a b + b 2 = ( a + b ) 2
or a 2 − 2 a b + b 2 = ( a − b ) 2 We can see that x 2 = a 2 and 2 a b = 6 x So all we need to condense this into ( a + b ) 2 is a b 2 term We know that 2 b = 6 as x = a
so b = 3
and b 2 = 9 So if we put the b 2 term in we get x 2 + 6 x + 9 − 9 = ( x + 3 ) 2 − 9 We include the ± 9 because we have to net add nothing to the equation so 9 − 9 = 0 so we really haven't added anything