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

Answer 2

Recall that

`√(x^2)=|x|`

which means

`√(4x^2)=√((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`.