Question

Find all values of x where sqrt(4x^2)-sqrt(x^2)=6.

Answer 1

Recall that

$\sqrt{x^2}=|x|$

which means

$\sqrt{4x^2}=\sqrt{(2x)^2}=|2x|$

So we have the equation

$|2x|-|x|=6$

This simplifies a bit:

$2|x|-|x|=|x|=6$

So there are two solutions here, $x=6$ and $x=-6$.

Answer 2

Recall that

\sqrt{x^2}=|x|

which means

\sqrt{4x^2}=\sqrt{(2x)^2}=|2x|

So we have the equation

|2x|-|x|=6