Example 9. If the inequality $x^{2}-2 a x+a^{2}+b \geqslant 0$ holds for any real number, then the range of values for $b$ is $\qquad$
(1987, Baoji City Junior High School Mathematics Competition)
Solve: Since the coefficient of the quadratic term is greater than zero, to make the solution set of the inequality the set of all real numbers, it is only necessary that
$$
\Delta=4 a^{2}-4\left(a^{2}+b\right) \leqslant 0 .
$$

Solving for the range of $b$ yields $b \geqslant 0$.