How do you find the value of a such that $y^2 +12y + a$ is a perfect square?

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Answer 1 · 2015-04-07T17:10:11

$(y+n)^2 = y^2+2ny+n^2$

If the coefficient of $y$ in a perfect square is $12$
then
$2n = 12$
$rarr n= 6$
and
$n^2 = 36$

$y^2+12y+36 = (y+6)^2$

$a=36$
makes $y^2+12y+a$ a perfect square

How do you find the value of a such that y^2 +12y + ay^2 +12y + a is a perfect square?