407. Rationalize $y=\sqrt{a^{2}+b x+c x^{2}}$ by the substitution $y=a+x z$.
407. We square:

$$
a^{2}+b x+c x^{2}=a^{2}+2 a x z+x^{2} z^{2}
$$

from which

$$
x=\frac{b-2 a z}{z^{2}-c}
$$

therefore, $a+x z=\frac{b z-a z^{2}-a c}{z^{2}-c}$.