2. Solve the equation $\left(x^{2}-|x|-2\right)^{2}+\sqrt{|2 x+1|-3}=0$.
# Solution

Since each term of the original equation is non-negative, the equation can have solutions if and only if both terms are equal to zero. We obtain the equivalent system of equations

$$
\left\{\begin{array}{l}
x^{2}-|x|-2=0 \\
|2 x+1|-3=0
\end{array}\right.
$$

The solution to this system is $x=-2$.

## Criteria

The equivalent system is formulated and justified, but solved incorrectly - 4 points. The equivalent system is formulated and solved, but not justified - 5 points.

The equivalent system is formulated, but not justified and solved with an error - 3 points.