What does it mean to write Q as a function of $\displaystyle x_1$ and $\displaystyle x_2$? Is the following what they are asking for:

$\displaystyle Q(x) = (x_1 x_2) \begin{pmatrix}4 & 3 \\ 3 & 5 \end{pmatrix} \begin{pmatrix} x_1\\ x_2 \end{pmatrix}$

$\displaystyle = 4x_1^2 + 5x^2_2 +6x_1x_2$

Is this correct so far? And how do I need to "complete the square" to show that Q(x)>0? (I don't have any notes on this...)