Answer
{$7-i\sqrt {21},7+i\sqrt {21}$}
Work Step by Step
We know that if $x^{2}=a$, then $x=\pm \sqrt{a}$. Thus, we obtain:
Step 1: $(x-7)^{2}=-21$
Step 2: $x-7=\pm \sqrt {-21}$
Step 3: $x-7=\pm \sqrt {-1\times21}$
Step 4: $x-7=\pm (\sqrt {-1}\times\sqrt {21})$
Step 5: $x-7=\pm (i\times\sqrt {21})$ [as $i=\sqrt {-1}$]
Step 6: $x-7=\pm (i\sqrt {21})$
Step 7: $x=7\pm (i\sqrt {21})$
Step 8: $x=7+i\sqrt {21}$ or $x=7-i\sqrt {21}$
Therefore, the solution set is {$7-i\sqrt {21},7+i\sqrt {21}$}.
