The equation $x^2+P=0$, where $P$ is an integer, has 2 integer solutions for $x$. Which of the following is a possible value of $P$ ?

$-48$

$-36$

$-10$

$36$

$48$

Approach 1

We can inspect each option:

$$ x^2-48 =0 $$ $$ x^2-36=0 $$ $$ x^2-10 = 0 $$ $$ x^2+36=0 $$ $$ x^2+48=0 $$

Only the second one, when $x=6$ and $x=-6$, seems appropriate.

Approach 2

$$ x^2+P = 0 $$ $$ x^2= -P $$ $$ x = \pm \sqrt{-P} $$

We will obtain two solutions if P is a negative perfect square.