Solve the following quadratic equations for x: 1. x² = 64 2. x² + 8x = 0 3. x² + 8x + 16 = 0 4. x² = 225 5. x² = 8x 6. x² = 5x - 6 7. x² - 4 = 0 8. (x - 1) * (-x - 4) = 0 9. 4x² - 20x = 0 10. 2x² - 9x - 5 = 0 11. x² + 16 = 0 12. x² - 4x + 16 = 0

Решение:

1. \( x^2 = 64 \)
   \( x = \pm\sqrt{64} \)
   \( x = \pm 8 \)
2. \( x^2 + 8x = 0 \)
   \( x(x + 8) = 0 \)
   \( x = 0 \) или \( x = -8 \)
3. \( x^2 + 8x + 16 = 0 \)
   \( (x + 4)^2 = 0 \)
   \( x = -4 \)
4. \( x^2 = 225 \)
   \( x = \pm\sqrt{225} \)
   \( x = \pm 15 \)
5. \( x^2 = 8x \)
   \( x^2 - 8x = 0 \)
   \( x(x - 8) = 0 \)
   \( x = 0 \) или \( x = 8 \)
6. \( x^2 = 5x - 6 \)
   \( x^2 - 5x + 6 = 0 \)
   \( (x - 2)(x - 3) = 0 \)
   \( x = 2 \) или \( x = 3 \)
7. \( x^2 - 4 = 0 \)
   \( x^2 = 4 \)
   \( x = \pm\sqrt{4} \)
   \( x = \pm 2 \)
8. \( (x - 1) \cdot (-x - 4) = 0 \)
   \( x - 1 = 0 \) или \( -x - 4 = 0 \)
   \( x = 1 \) или \( x = -4 \)
9. \( 4x^2 - 20x = 0 \)
   \( 4x(x - 5) = 0 \)
   \( x = 0 \) или \( x = 5 \)
10. \( 2x^2 - 9x - 5 = 0 \)
    \( D = (-9)^2 - 4(2)(-5) = 81 + 40 = 121 \)
    \( x = \frac{9 \pm \sqrt{121}}{2 \cdot 2} = \frac{9 \pm 11}{4} \)
    \( x_1 = \frac{9 + 11}{4} = \frac{20}{4} = 5 \), \( x_2 = \frac{9 - 11}{4} = \frac{-2}{4} = -0.5 \)
11. \( x^2 + 16 = 0 \)
    \( x^2 = -16 \)
    Действительных корней нет.
12. \( x^2 - 4x + 16 = 0 \)
    \( D = (-4)^2 - 4(1)(16) = 16 - 64 = -48 \)
    Действительных корней нет.

Ответ: 1. \( x = \pm 8 \); 2. \( x = 0, x = -8 \); 3. \( x = -4 \); 4. \( x = \pm 15 \); 5. \( x = 0, x = 8 \); 6. \( x = 2, x = 3 \); 7. \( x = \pm 2 \); 8. \( x = 1, x = -4 \); 9. \( x = 0, x = 5 \); 10. \( x = 5, x = -0.5 \); 11. Действительных корней нет; 12. Действительных корней нет.