How to solve a system of nonlinear equations where there are more equations than variables?

Question

I have a system of equations, which is given by: \begin{equation} \begin{pmatrix} a_1^2 \\ a_1a_2 \\ a_1a_3 \\ a_2a_1 \\ a_2^2 \\ a_2a_3 \\ a_3a_1 \\ a_3a_2 \\ a_3^2 \end{pmatrix}=\begin{pmatrix} k_1 \\ k_2 \\ k_3 \\ k_4 \\ k_5 \\ k_6 \\ k_7 \\ k_8 \\ k_9 \end{pmatrix} \end{equation} where $a_1,a_2,a_3$ are unknowns and $k_i ,i=1,2,...9$ are knowns. How can I obtain $a_j, j=1,2,3$? The problem I am facing is, if I only consider $a_1^2,a_2^2,a_3^2$, then the corresponding $k_1,k_5,k_9$ might be negative leading to complex values and hence that is not acceptable. I need to be evaluate this (i.e find $a_j, j=1,2,3$) at every time instant in my simulation. Any workarounds? Thanks for your time and consideration!