$x^{2} + 3 | x | + 2 = 0$ Find the value of $x$ .

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Solution

when $x < 0 | x | = - x$
$x^{2} - 3 x + 2 = 0$
$x^{2} - 2 x - x + 2 = 0$
$x (x - 2) - 1 (x - 2) = 0$
$(x - 2) (x - 1) = 0$
$x = 2, 1$
when $x > 0 | x | = x$
$x^{2} + 3 x + 2 = 0$
$x^{2} + 2 x + x + 2 = 0$
$x (x + 2) 1 (x + 2) = 0$
$(x + 2) (x + 1) = 0$
$x = - 2, - 1$

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