[tex] \it 12(x + 1) ^{2} = (6 + 2 \sqrt{3} ) ^{2} \\ \\ \it (x + 1) ^{2} = \frac{(6 + 2\sqrt{3} ) ^{2} }{12} \\ \\ \it (x + 1) ^{2} = \frac{(6 + 2 \sqrt{3}) ^{2} }{( \sqrt{12}) ^{2} } \\ \\ \it (x + 1) ^{2} = ( \frac{6 + 2 \sqrt{3} }{ \sqrt{12} } ) ^{2} \\ \\ \it (x + 1) ^{2} = ( \frac{6 + 2 \sqrt{3} }{2 \sqrt{3} } )^{2} \\ \\ \it x + 1 = \pm \: ( \frac{6 + 2 \sqrt{3} }{2 \sqrt{3} } ) \\ \\ \it x + 1 = \frac{6 + 2 \sqrt{3} }{2 \sqrt{3} } \\ \\ \it x = \frac{6 + 2 \sqrt{3} }{2 \sqrt{3} } \: - \: ^{2 \sqrt{3} )} 1 \\ \\ \it x = \frac{6 + 2 \sqrt{3} - 2 \sqrt{3} }{2 \sqrt{3} } \\ \\ \it x = \frac{6}{2 \sqrt{3} } ^{(2} = > \\ \\ \it x = \: ^{ \sqrt{3} )} \frac{3}{ \sqrt{3} } \\ \\ \it x = \frac{3 \sqrt{3} }{3} \\ \\ \it \mathbf{x = \sqrt{3} } \\ \\ \it x + 1 = - \frac{6 + 2 \sqrt{3} }{2 \sqrt{3} } \\ \\ \it x = - \frac{6 + 2 \sqrt{3} }{2 \sqrt{3} } \: - \: ^{2 \sqrt{3} )} 1 \\ \\ \it x = \frac{ - 6 - 2 \sqrt{3} - 2 \sqrt{3} }{2 \sqrt{3} } \\ \\ \it x = \frac{ - 6 - 4 \sqrt{3} }{2 \sqrt{3} } \\ \\ \it x = \frac{2( - 3 - 2 \sqrt{3}) }{2 \sqrt{3} } \\ \\ \it x = \: ^{ \sqrt{3}) } \: \frac{ - 3 - 2 \sqrt{3} }{ \sqrt{3} } \\ \\ \it x = \frac{ - 3 \sqrt{3} - 6 }{3} \\ \\ \it x = \frac{3( - \sqrt{3} - 2) }{3} = > \\ \\ \it \mathbf{x = - \sqrt{3} - 2}[/tex]
