Chapter 10 - Radical Expressions and Equations - 10-3 Operations with Radial Expressions - Practice and Problem-Solving Exercises - Page 617: 38

$x =10\sqrt{2}+10 \approx 24.1$

Cross Multiply: $\frac{5\sqrt{2}}{\sqrt{2}-1}=\frac{x}{\sqrt{2}}, 5\sqrt{2}\sqrt{2}=x(\sqrt{2}-1) , 10=x(\sqrt{2}-1) , x=\frac{10}{\sqrt{2}-1}\cdot \frac{\sqrt{2}+1}{\sqrt{2}+1}= \frac{10\sqrt{2}+10}{2-1}=10\sqrt{2}+10$