Answer
{$6-5i,6+5i$}
Work Step by Step
We know that if $x^{2}=a$, then $x=\pm \sqrt{a}$. Thus, we obtain:
Step 1: $(x-6)^{2}=-25$
Step 2: $x-6=\pm \sqrt {-25}$
Step 3: $x-6=\pm \sqrt {-1\times25}$
Step 4: $x-6=\pm \sqrt {-1}\times\sqrt {25}$
Step 5: $x-6=\pm (i\times5)$ [as $i=\sqrt{-1}$]
Step 6: $x-6=\pm 5i$
Step 7: $x-6=5i$ or $x-6=-5i$
Step 8: $x=6+5i$ or $x=6-5i$
The solution set is {$6-5i,6+5i$}.
