[tex]1.) \:{3x}^{2} - 1 = 11[/tex]

[tex] {3x}^{2} - 1 + 1 = 11 + 1[/tex]

[tex] {3x}^{2} = 12[/tex]

[tex] \frac{ {3x}^{2} }{3} = \frac{12}{3} [/tex]

[tex] {x}^{2} = 4[/tex]

[tex] \sqrt{ {x}^{2} } = \sqrt{4} [/tex]

[tex]x = 2[/tex]

[tex]2.) {9x}^{2} - 6 = 20[/tex]

[tex] {9x}^{2} - 6 + 6 = 20 + 6[/tex]

[tex] {9x}^{2} = 26[/tex]

[tex] \frac{ {9x}^{2} }{9} = \frac{26}{9} [/tex]

[tex] {x}^{2} = \frac{26}{9} [/tex]

[tex] \sqrt{ {x}^{2} } = \sqrt{ \frac{26}{9} } [/tex]

[tex]x = \frac{ \sqrt{26} }{3} \: \:or \: \: 1.70[/tex]

[tex] 3.) \: {9x}^{2} - 6 = 0[/tex]

[tex] {9x}^{2} - 6 + 6 = 0 + 6[/tex]

[tex] {9x}^{2} = 6[/tex]

[tex] \frac{ {9x}^{2} }{9} = \frac{6}{9} [/tex]

[tex] {x}^{2} = \frac{6}{9} [/tex]

[tex] \sqrt{ {x}^{2} } = \sqrt{ \frac{6}{9} } [/tex]

[tex]x = \frac{3 \sqrt{2} }{3} \: \: or \: \: 1.41[/tex]

[tex]4.) \: {5x}^{2} - 2 = 28[/tex]

[tex] {5x}^{2} - 2 + 2 = 28 + 2[/tex]

[tex] {5x}^{2} = 30[/tex]

[tex] \frac{ {5x}^{2} }{5} = \frac{30}{5} [/tex]

[tex] {x}^{2} = 6[/tex]

[tex] \sqrt{ {x}^{2} } = \sqrt{6} [/tex]

[tex]x = \sqrt{6} \: \: or \: \: 2.45[/tex]

[tex]5.) \: 2{(x - 5)}^{2} = 32[/tex]

[tex] \frac{2 {(x - 5)}^{2} }{2} = \frac{32}{2} [/tex]

[tex] {(x - 5)}^{2} = 8[/tex]

[tex] \sqrt{ {(x - 5)}^{2} } = \sqrt{8} [/tex]

[tex]x - 5 = 2 \sqrt{2} [/tex]

[tex]x - 5 + 5 = 2 \sqrt{2} + 5[/tex]

[tex]x = 2 \sqrt{2} + 5 \: \: or \: \: 7.83[/tex]