the first equation is,
[tex]\begin{gathered} -5x^2=-500^{} \\ 5x^2=500 \\ x^2=\frac{500}{5} \end{gathered}[/tex]solve further,
[tex]\begin{gathered} x^2=\frac{500}{5} \\ x^2=100 \\ x=\sqrt[]{100}=\pm10 \\ x=10,-10 \end{gathered}[/tex]the second equation is
[tex]\begin{gathered} (x+2)^2=169 \\ x+2=\sqrt[]{169} \\ x+2=\pm13 \\ x=13-2,\text{ -13-2} \\ x=11,-15 \end{gathered}[/tex]the equation third is.
[tex]\begin{gathered} x^2-49=0 \\ x^2=49 \\ x=\sqrt[]{49} \\ x=\pm7 \\ x=7,-7 \end{gathered}[/tex]the fourth equation is,
[tex]\begin{gathered} x^2=25 \\ x^2=\sqrt[]{25} \\ x=\pm5 \\ x=5,-5 \end{gathered}[/tex]