5x^2=100

To be precisely correct we need to include -2√5 as a solution, too.

5x^2=100

$$\begin{array}{rcl} 5\cdot x^2 &=& 100 \qquad| \quad :5 \\ x^2 &=& 20 \\ x^2 &=& 20 \qquad | \quad \sqrt\\ x &=& \sqrt {20} \\ x &=& \sqrt {4\cdot 5} \\ x &=& \sqrt {4} \cdot \sqrt {5} \qquad | \qaud \sqrt{4} = 2\\ x &=& 2 \cdot \sqrt {5} \\ \end{array}$$

That working out is perfectly fine!

Good spotting Chris :)