Given $a \neq 0,$ solve for $x$ in
\[\begin{vmatrix} x + a & x  & x \\ x & x + a & x \\ x & x & x + a \end{vmatrix} = 0.\]Give your answer in terms of $a.$
Question:
Given $a \neq 0,$ solve for $x$ in
\[\begin{vmatrix} x + a & x  & x \\ x & x + a & x \\ x & x & x + a \end{vmatrix} = 0.\]Give your answer in terms of $a.$
Answer:
Let's think step by step.

user
-\frac{a}{3}
Given $a \neq 0,$ solve for $x$ in
\[\begin{vmatrix} x + a & x  & x \\ x & x + a & x \\ x & x & x + a \end{vmatrix} = 0.\]Give your answer in terms of $a.$
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