Hi! I need some help on understanding this proof:

If the equation $\displaystyle x^2 + 2(k+2)x +9k = 0 $ has equal roots, find k.

The condition for equal roots gives

$\displaystyle (k+2)^2 = 9k $

$\displaystyle k^2 - 5k + 4 =0 $

$\displaystyle (k-4)(k-1) = 0 $

$\displaystyle k=4 , k=1 $

The proof makes sense: When k = 4, for example, we get $\displaystyle x^2 + 12x + 36 $ and this will give equal roots if $\displaystyle b^2 - 4ac = 0 $ which it does since $\displaystyle 144 - 144 = 0 $

But I still don't understand where the first line of the proof,

$\displaystyle (k+2)^2 = 9k $, comes from

From *Higher Algebra, *H.S Hall & Knight