Решите уравнение: (x-7)(x+7)+(x-2)^2=11x+30-(x+5)^2.

Ответ:

\[(x - 7)(x + 7) + (x - 2)^{2} =\]

\[= 11x + 30 - (x + 5)^{2}\]

\[x^{2} - 49 + x^{2} - 4x + 4 - 11x - 30 =\]

\[= - x^{2} - 10x - 25\]

\[2x^{2} + x^{2} - 15x + 10x - 75 + 25 =\]

\[= 0\]

\[3x^{2} - 5x - 50 = 0\]

\[D = 25 + 600 = 625\]

\[x_{1} = \frac{5 + 25}{6} = \frac{30}{6} = 5;\ \ \ \]

\[x_{2} = \frac{5 - 25}{6} = - \frac{20}{6} = - \frac{10}{3} =\]

\[= - 3\frac{1}{3}.\]