Question 413·Hard·Advanced Math

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In the $xy$ -plane, consider the system of equations

\begin{cases} x^2 + y^2 = 20 \\[4pt] y = \dfrac{1}{2}x + b \end{cases}

where $b$ is a real constant. The system has exactly one real solution. What is the sum of all possible values of $b$ ?

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