\[\sqrt{7 + \sqrt{6 - \sqrt{x}}} = 3\]
\[7 + \sqrt{6 - \sqrt{x}} = 9\]
\[\sqrt{6 - \sqrt{x}} = 2\]
\[6 - \sqrt{x} = 4\]
\[\sqrt{x} = 2\]
\[x = 4.\]