Question

Extracting the roots

a^2+12a+36=49

Answer 1

\[(a+6)^2=49\]
\[a+6=7\] so
\[a=1\]
OR
\[a+6=-7\]so
\[a=-13\]

Answer 2

trick was to recognize that
\[a^2+12a+36=(a+6)^2\] and you see it because
\[a^2\] is the square of
\[a\]

6 is the square of 36 and 12a is 2 times 6 times a

Answer 3

Of course, using the general formula for solving quadratic equations works as well, but recognizing the square of a binomial is indeed a handy way to solve some equations faster. :)

Answer 4

It is actually much easier to move the 49 over first
\[a^2 + 12a - 13 = 0\]
\[(a+13)(a-1)=0\]

Answer 5

JethroKuan: I think it depends _a lot_ on the specific curriculum and school how much people practise factorising. I can see how you did that but by no means would have I did that myself. :) That method takes some practice of routines and tricks.