Решите уравнение: x^2+5x-14=0.

Ответ:

\[x² + 5x - 14 = 0\]

\[a = 1,\ \ b = 5,\ \ c = - 14.\]

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

\[= 5^{2} - 4 \cdot 1 \cdot ( - 14) =\]

\[= 25 + 56 = 81\]

\[x_{1,2} = \frac{- b \pm \sqrt{D}}{2a}\]

\[x_{1} = \frac{- 5 + \sqrt{81}}{2 \cdot 1} =\]

\[= \frac{- 5 + 9}{2} = \frac{4}{2} = 2\]

\[x_{2} = \frac{- 5 - \sqrt{81}}{2 \cdot 1} = \frac{- 5 - 9}{2} =\]

\[= - \frac{14}{2} = - 7\]

\[Ответ:x = 2;\ x = - 7.\]