7. As shown in Figure 4, in the right triangle $\triangle ABC$, $\angle ACB=90^{\circ}$, $AC=b$, $AB=c$. If $D$ and $E$ are points on $AB$ and the extension of $AB$ respectively, such that $BD=BC$, $CE \perp CD$, then the quadratic equation with the lengths of $AD$ and $AE$ as roots is ( ).
(A) $x^{2}-2 c x+b^{2}=0$
(B) $x^{2}-c x+b^{2}=0$
(C) $x^{2}-2 c x+b=0$
(D) $x^{2}-c x+b=0$
7. (A)