При каждом значении параметра k решите уравнение: x^2+(k-6)x-6k=0.

\[x² + (k - 6)x - 6k = 0\]

\[D = (k - 6)^{2} - 4 \bullet ( - 6k) =\]

\[= k^{2} - 12k + 36 + 24k =\]

\[= k^{2} + 12k + 36 = (k + 6)²\]

\[k \neq - 6 \Longrightarrow D > 0:\]

\[x_{1} = \frac{- (k + 6) + k + 6}{2} =\]

\[= \frac{- k + 6 + k + 6}{2} = \frac{12}{2} = 6\]

\[x_{1} = \frac{- (k + 6) - (k + 6)}{2} =\]

\[= \frac{- k + 6 - k - 6}{2} = - \frac{2k}{2} = - k.\]

\[k = - 6 \Longrightarrow D = 0:\]

\[x = \frac{- (k - 6)}{2} = \frac{- ( - 6 - 6)}{2} =\]

\[= \frac{12}{2} = 6.\]

\[Ответ:x = 6\ и\ \ x = - k\ при\ \]

\[k \neq - 6;\ \ \]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ x = 6\ при\ \ k = - 6.\]