Existence, Uniqueness and Counterexamples · Hard problem

A student solves $\sqrt{x + 3} = x - 3$ by squaring: $x + 3 = x^2 - 6x + 9$, so $x^2 - 7x + 6 = 0$, so $x = 1$ or $x = 6$. How many real solutions does the ORIGINAL equation have?