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

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Answer 1 · 2016-06-02T20:51:54

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

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

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

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