We are told to find the solution of
[tex]x^2=-7[/tex]To solve, we will find the square root of both sides
[tex]x=\sqrt[]{-1}\times\pm\sqrt[]{7}[/tex]But we will use the relationship
[tex]\sqrt[]{-1}=i[/tex]Thus, we have
[tex]\begin{gathered} x=\pm\sqrt[]{7}\times i \\ x=\pm\sqrt[]{7}i \end{gathered}[/tex]Thus, the answer is
[tex]\begin{gathered} x=\sqrt[]{7}i \\ x=-\sqrt[]{7}i \end{gathered}[/tex]