\[2\sqrt{18} + 5\sqrt{50} - \frac{1}{4}\sqrt{32} - 7\sqrt{2} =\]
\[= 2\sqrt{9 \cdot 2} + 5\sqrt{25 \cdot 2} - \frac{1}{4}\sqrt{16 \cdot 2} - 7\sqrt{2} =\]
\[= 2 \cdot 3\sqrt{2} + 5 \cdot 5\sqrt{2} - \frac{1}{4} \cdot 4\sqrt{2} - 7\sqrt{2} =\]
\[= 6\sqrt{2} + 25\sqrt{2} - \sqrt{2} - 7\sqrt{2} = 22\sqrt{2}.\]