To factor the expression over the complex numbers, let's fin its roots, then we will be able to write it in the generic form of a factored polynomial as follows:
[tex](x-a)(x-b)[/tex]
Where a and b stand for the roots of the polynomial.
[tex]\begin{gathered} x^2+50=0\to x^2=-50 \\ \to x_{1,2}=\pm\sqrt[]{-50} \\ x_1=i\sqrt[]{50} \\ x_2=-i\sqrt[]{50} \end{gathered}[/tex]
From this, we can rewrite the polynomial as follows:
[tex]x^2+50=(x+i\sqrt[]{50})(x-i\sqrt[]{50})[/tex]
