Let $2 \times 2$ matrix $A=(2,-2,-2,5)$ Find a $2 \times 2$ matrix M such that $A=M^tM$

Question

I was thinking to go this way:

Determine if $A$ is positive definite, if each of the eigenvalues of $A$ are positive. Then we diagonalize $A$. $A=PDP^T$. Thus we can let $C$ be the diagonal matrix whose diagonal entry is $√λ$. Thus $CC = D$ Now let $B = PCP^T$, and it remains to show that $B^TB = A$.

Any thoughts?