[tex]\large\boxed{\begin{array}{l}\sf a)~ x^2-25=0\\\sf x^2=25\\\sf x=\pm\sqrt{25}\\\sf x=\pm5\implies S=\{-5,5\}\\\sf b)~x^2-100=0\\\sf x^2=100\\\sf x=\pm\sqrt{100}\\\sf x=\pm10\implies S=\{-10,10\}\\\sf c)~2x^2-900=0\\\sf 2x^2=900\\\sf x^2=\dfrac{900}{2}\\\sf x^2=450\\\sf x=\pm\sqrt{450}\\\sf x=\pm\sqrt{225\cdot2}\\\sf x=\pm15\sqrt{2}\implies S=\{-15\sqrt{2},15\sqrt{2}\}\end{array}}[/tex]
[tex]\large\boxed{\begin{array}{l}\sf d)~3x^2-75=0\\\sf 3x^2=75\\\sf x^2=\dfrac{75}{3}\\\\\sf x^2=25\\\sf x=\pm\sqrt{25}\\\sf x=\pm15\implies S=\{-15,15\}\\\sf e)~ x^2-625=0\\\sf x^2=625\\\sf x=\pm\sqrt{625}\\\sf x=\pm25\implies S=\{-25,25\}\\\sf f)~ x^2-289=0\\\sf x^2=289\\\sf x=\pm\sqrt{289}\\\sf x=\pm17\implies S=\{-17,17\}\end{array}}[/tex]
[tex]\large\boxed{\begin{array}{l}\sf g)~x^2-529=0\\\sf x^2=529\\\sf x=\pm\sqrt{529}\\\sf x=\pm23\implies S=\{-23,23\}\\\sf h)~ x^2-1225=0\\\sf x^2=1225\\\sf x=\pm\sqrt{1225}\\\sf x=\pm35\implies S=\{-35,35\}\\\sf i)~ x^2-2=0\\\sf x^2=2\\\sf x=\pm\sqrt{2}\implies S=\{-\sqrt{2},\sqrt{2}\}\end{array}}[/tex]
