Question

solve x^2+5x+6=0 by completing the square

Answer 1

we need to add zero to this in order for it to be useful

Answer 2

\[(x+a)(x+b)=x^2+(a+b)x+ab\]
if b=a we have a perfect square (a complete square)
\[(x+a)(x+a)=x^2+(a+a)x+aa\]\[(x+a)(x+a)=x^2+(2a)x+a^2\]
notice that the last term of a completed square is half the middle term, squared

\[(x+3)(x+3)=x^2+(a+a)x+aa\]\[(x+a)(x+a)=x^2+2(3)x+3^2\]

and that is the key to completing a square

Answer 3

.... copy paste failed :) last part should have been

\[(x+3)(x+3)=x^2+2(3)x+3^2\]