1. Решите уравнения: а) -3x - 9 = 2x б) x + 3 = -9x в) 4(x - 2) = -1 г) 5(x - 6) = 2 д) 8x^2 = 72x е) 6x^2 = 36x ж) x^2 - 81 = 0 з) x^2 - 49 = 0 и) x^2 - 8x + 12 = 0 к) x^2 - 9x + 8 = 0

Решение:

1. а) -3x - 9 = 2x
   \( -3x - 2x = 9 \)
   \( -5x = 9 \)
   \( x = - \frac{9}{5} \)
2. б) x + 3 = -9x
   \( x + 9x = -3 \)
   \( 10x = -3 \)
   \( x = - \frac{3}{10} \)
3. в) 4(x - 2) = -1
   \( 4x - 8 = -1 \)
   \( 4x = -1 + 8 \)
   \( 4x = 7 \)
   \( x = \frac{7}{4} \)
4. г) 5(x - 6) = 2
   \( 5x - 30 = 2 \)
   \( 5x = 32 \)
   \( x = \frac{32}{5} \)
5. д) 8x^2 = 72x
   \( 8x^2 - 72x = 0 \)
   \( 8x(x - 9) = 0 \)
   \( x = 0 \) или \( x - 9 = 0 \)
   \( x = 0 \) или \( x = 9 \)
6. е) 6x^2 = 36x
   \( 6x^2 - 36x = 0 \)
   \( 6x(x - 6) = 0 \)
   \( x = 0 \) или \( x - 6 = 0 \)
   \( x = 0 \) или \( x = 6 \)
7. ж) x^2 - 81 = 0
   \( x^2 = 81 \)
   \( x = \pm \sqrt{81} \)
   \( x = \pm 9 \)
8. з) x^2 - 49 = 0
   \( x^2 = 49 \)
   \( x = \pm \sqrt{49} \)
   \( x = \pm 7 \)
9. и) x^2 - 8x + 12 = 0
   \( D = (-8)^2 - 4 \cdot 1 \cdot 12 = 64 - 48 = 16 \)
   \( x_1 = \frac{8 + \sqrt{16}}{2} = \frac{8 + 4}{2} = 6 \)
   \( x_2 = \frac{8 - \sqrt{16}}{2} = \frac{8 - 4}{2} = 2 \)
10. к) x^2 - 9x + 8 = 0
    \( D = (-9)^2 - 4 \cdot 1 \cdot 8 = 81 - 32 = 49 \)
    \( x_1 = \frac{9 + \sqrt{49}}{2} = \frac{9 + 7}{2} = 8 \)
    \( x_2 = \frac{9 - \sqrt{49}}{2} = \frac{9 - 7}{2} = 1 \)

Ответ: а) \( x = -1.8 \); б) \( x = -0.3 \); в) \( x = 1.75 \); г) \( x = 6.4 \); д) \( x = 0, x = 9 \); е) \( x = 0, x = 6 \); ж) \( x = \pm 9 \); з) \( x = \pm 7 \); и) \( x_1 = 6, x_2 = 2 \); к) \( x_1 = 8, x_2 = 1 \).