Решите уравнение: (3x+1)^2-100=0.

\[(3x + 1)^{2} - 100 = 0\]

\[(3x + 1 - 10)(3x + 1 + 10) = 0\]

\[(3x - 9)(3x + 11) = 0\]

\[3x - 9 = 0\ \ \ \ \ \ \ 3x + 11 = 0\]

\[3x = 9\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3x = - 11\]

\[x = 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - \frac{11}{3} = - 3\frac{2}{3}\]

\[Ответ:x = 3;\ x = - 3\frac{2}{3}.\]