Real $2\times 2$ matrix $X$ such that $X^2 + 2X= -5I$ Find a real $2\times 2$ matrix $X = \left(\begin{matrix} a& b\\ c & d\end{matrix}\right)$ such that $X^2 + 2X = -5I.$ 
With this question I'm kinda lost with the $2X$ part but a full explanation or a little bit of a lead would be greatly appreciated. 

Expanded you get that
\begin{matrix}
        5 + a (2 + a) + b c & b (2 + a + d) \\
        c (2 + a + d) & 5 + b c + d (2 + d)  \\
        \end{matrix} 
equals 0.
Solving using Mathematica 9
X = {{a, b}, {c, d}};
Id = IdentityMatrix[2];
Solve[ X.X + 2 X == -5 Id, {a, b, c, d}]

Atleast these are possible answers:
{a -> -1 - 2i, b -> 0, c -> 0, d -> -1 - 2i}, 
{a -> -1 - 2i, b -> 0, c -> 0, d -> -1 + 2i},
{a -> -1 + 2i, b -> 0, c -> 0, d -> -1 - 2i}, 
{a -> -1 + 2i, b -> 0, c -> 0, d -> -1 + 2i}

