Find all real numbers $a$ such that the equation
\[x^3 - ax^2 - 2ax + a^2 - 1 = 0\]has exactly one real solution in $x.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find all real numbers $a$ such that the equation
\[x^3 - ax^2 - 2ax + a^2 - 1 = 0\]has exactly one real solution in $x.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\left( -\infty, \frac{3}{4} \right)
Find all real numbers $a$ such that the equation
\[x^3 - ax^2 - 2ax + a^2 - 1 = 0\]has exactly one real solution in $x.$
train