Question

How do you solve `(2x-1)^2 +｜2x-1｜-12 =0`?

Answer 1

`{x = 1, x = -2}`

Explanation:

Posing `y = abs(2x-1)`
and solving
`y^2+y-12=0`
we have `{y = -4, y = 3}`.

Choosing `y = 3` as the viable solution, we have then
`abs(2x-1)=3` which is equivalent to

#{ (2x-1 = 3), (2x-1 = -3) :}#

with the solutions

`{x = 1, x = -2}`