Arrange, Then Root

$x^{2}-49 = 0$ is a difference of squares, so you could factor it. There is a faster way. Move the 49 to the other side to get $x^{2} = 49$, then take the square root of both sides: $x = \pm 7$.

Both methods give the same answers, 7 and -7. Factoring gives $\left(x+7\right)\left(x-7\right) = 0$, and then one factor must be zero. Taking square roots of $x^{2} = 49$ gives $x = \pm 7$ in one step.

The first step is the same as in factoring: get the squared term alone on one side. Move the constant to the other side so that $x^{2}$ stands by itself, and only then take the square root.