<s>[INST] How to solve the equation $x^2 + 4 |x| - 4 = 0$ How do I get the value of x from the equation that is provided
 [/INST] Putting $x=a+ib$ where $a,b$ are real
we get $\sqrt{a^2+b^2}=4-(a+ib)^2=4+b^2-a^2-2abi$
Equating the imaginary parts $ b=0$
Now for real $x,$ 
$$|x|= \begin{cases} +x &\mbox{if } x\ge0 \\
-x & \mbox{if } x<0 \end{cases}$$
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