\[x^{2} + bx + 36 = 0 \Longrightarrow\]
\[\Longrightarrow \ единственный\ корень\ при\ \]
\[D = 0.\]
\[D = b^{2} - 4 \cdot 1 \cdot 36 = b^{2} - 144 =\]
\[= 0\]
\[b^{2} - 144 = 0\]
\[(b - 12)(b + 12) = 0\]
\[Ответ:при\ b = 12;\ b = - 12.\]