Question

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

Answer 1

`(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