Answer
The equation is an identity, true for all real values of $x$.
Work Step by Step
The equation $|x|=\sqrt{x^{2}}$ has infinitely many solutions because if we solve it, we get an identity:
$|x|$ implies:
$|x|=x$ (if x is positive) or $|x|=-x$ (if x is negative)
Similarly:
$\sqrt{x^{2}}$ implies:
$\sqrt{x^{2}}=x$ (if x is positive) or $\sqrt{x^{2}}=-x$ (if x is negative)
Hence the two sides equal each other (identity). In other words, the equation is true for all real values of $x$ (infinite solutions).
