Why is $2x-1=7$ not $x=-4 \text{ or } x=4$ How would you explain why $3(2x-1)^2=147$, is $2x-1=7 \text{ or } 2x-1=-7$. But not $2x=8 \text{ so } x=4 \text{ or } x=-4$? 

$$ 3(2x-1)^2=147 $$
$$ (2x-1)^2=\frac{147}{3} $$
$$ (2x-1)^2=49 $$
$$ (2x-1)^2=(\pm 7)^2 $$
$$ \sqrt{(2x-1)^2}=\sqrt{(\pm 7)^2} $$
$$ 2x-1=\pm 7$$
$$ 2x=1\pm 7$$
$$ x=\frac{1\pm 7}{2}$$
Therefore 
$$ x_1=\frac{1+ 7}{2}=\frac82=4$$
$$ x_2=\frac{1- 7}{2}=-\frac62=-3$$
