x² - 8x = -16 (2x−1)(x + 2) = 42

Решим первое уравнение:

$$x^2 - 8x = -16$$

$$x^2 - 8x + 16 = 0$$

$$(x-4)^2 = 0$$

$$x = 4$$

Решим второе уравнение:

$$(2x-1)(x+2) = 42$$

$$2x^2 + 4x - x - 2 = 42$$

$$2x^2 + 3x - 44 = 0$$

$$D = b^2 - 4ac = 3^2 - 4 \cdot 2 \cdot (-44) = 9 + 352 = 361$$

$$x_1 = \frac{-3 + \sqrt{361}}{4} = \frac{-3 + 19}{4} = \frac{16}{4} = 4$$

$$x_2 = \frac{-3 - \sqrt{361}}{4} = \frac{-3 - 19}{4} = \frac{-22}{4} = -\frac{11}{2} = -5.5$$

Ответ: x = 4, x = 4, x = -5.5