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

Apr 7, 2015

${\left(y + n\right)}^{2} = {y}^{2} + 2 n y + {n}^{2}$

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

${y}^{2} + 12 y + 36 = {\left(y + 6\right)}^{2}$

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