Answer
{$-7i,7i$}
Work Step by Step
We know that if $x^{2}=a$, then $x=\pm \sqrt{a}$. Thus, we obtain:
Step 1: $(x)^{2}=-49$
Step 2: $x=\pm \sqrt {-49}$
Step 3: $x=\pm \sqrt {-1\times49}$
Step 4: $x=\pm \sqrt {-1}\times\sqrt {49}$
Step 5: $x=\pm (i\times\sqrt {49})$ [as $i=\sqrt {-1}$]
Step 6: $x=\pm (i\times7)$
Step 7: $x=\pm (7i)$
Step 8: $x=7i$ or $x=-7i$
Therefore, the solution set is {$-7i,7i$}.
