C.  $x^2+10x+25=0$

$x^2+2\cdot x\cdot 5+5^2=0$

${\left(x+5\right)}^2=0$

$x+5=0$

$x=-5$

D.  ${\left(x-3\right)}^2-1=0$

${\left(x-3\right)}^2=1$

$x-3=1\text{lub}x-3=-1$

$x=4x=2$

$x\in \left\{2,4\right\}$

E.  ${\left(x-3\right)}^2+1=0$

${\left(x-3\right)}^2=-1$

Równanie sprzeczne.