№ 46. Решите уравнение: а) x² + 7x = 0; б) 2x - 4x² = 0; в) 6x² - 54x = 0; г) 4,5x² - 9x = 0; д) -1,2x - 4x² = 0; е) 0,81x² - 0,9x = 0; ж) 63x³ + 9x² = 0; з) 4x³ - 100x = 0.

Решение:

1. а) \( x^2 + 7x = 0 \)
   \( x(x + 7) = 0 \)
   \( x_1 = 0, x_2 = -7 \)
2. б) \( 2x - 4x^2 = 0 \)
   \( 2x(1 - 2x) = 0 \)
   \( x_1 = 0, x_2 = \frac{1}{2} \)
3. в) \( 6x^2 - 54x = 0 \)
   \( 6x(x - 9) = 0 \)
   \( x_1 = 0, x_2 = 9 \)
4. г) \( 4.5x^2 - 9x = 0 \)
   \( 4.5x(x - 2) = 0 \)
   \( x_1 = 0, x_2 = 2 \)
5. д) \( -1.2x - 4x^2 = 0 \)
   \( -4x(0.3 + x) = 0 \)
   \( x_1 = 0, x_2 = -0.3 \)
6. е) \( 0.81x^2 - 0.9x = 0 \)
   \( 0.9x(0.9x - 1) = 0 \)
   \( x_1 = 0, x_2 = \frac{1}{0.9} = \frac{10}{9} \)
7. ж) \( 63x^3 + 9x^2 = 0 \)
   \( 9x^2(7x + 1) = 0 \)
   \( x_1 = 0, x_2 = -\frac{1}{7} \)
8. з) \( 4x^3 - 100x = 0 \)
   \( 4x(x^2 - 25) = 0 \)
   \( 4x(x - 5)(x + 5) = 0 \)
   \( x_1 = 0, x_2 = 5, x_3 = -5 \)

Ответ: а) 0; -7; б) 0; 1/2; в) 0; 9; г) 0; 2; д) 0; -0.3; е) 0; 10/9; ж) 0; -1/7; з) 0; 5; -5.