Найдите корни уравнения: (x-1)^2=29-5x.

Ответ:

\[(x - 1)² = 29 - 5x\]

\[x^{2} - 2x + 1 - 29 + 5x = 0\]

\[x^{2} + 3x - 28 =\]

\[D = b^{2} - 4ac =\]

\[= 9 - 4 \cdot 1 \cdot ( - 28) =\]

\[= 9 + 112 = 121\]

\[x_{1} = \frac{- 3 + 11}{2} = \frac{8}{2} = 4\]

\[x_{2} = \frac{- 3 - 11}{2} = - \frac{14}{2} = - 7\]

\[Ответ:x = 4\ \ и\ \ \ x = - 7.\]