Solve the following quadratic equations for x: 1. x² = 49 2. x² - 8x = 0 3. x² - 10x + 25 = 0 4. x² - 169 = 0 5. x² = 3x 6. x² + 8x = 9 7. x² = 16 8. (x - 2) * (-x - 1) = 0 9. 7x² - 14x = 0 10. 2x² + 5x - 3 = 0 11. 4x² + 21 = 0 12. 3x² - 2x + 4 = 0

Решение:

1. \( x^2 = 49 \)
   \( x = \pm\sqrt{49} \)
   \( x = \pm 7 \)
2. \( x^2 - 8x = 0 \)
   \( x(x - 8) = 0 \)
   \( x = 0 \) или \( x = 8 \)
3. \( x^2 - 10x + 25 = 0 \)
   \( (x - 5)^2 = 0 \)
   \( x = 5 \)
4. \( x^2 - 169 = 0 \)
   \( x^2 = 169 \)
   \( x = \pm\sqrt{169} \)
   \( x = \pm 13 \)
5. \( x^2 = 3x \)
   \( x^2 - 3x = 0 \)
   \( x(x - 3) = 0 \)
   \( x = 0 \) или \( x = 3 \)
6. \( x^2 + 8x = 9 \)
   \( x^2 + 8x - 9 = 0 \)
   \( (x + 9)(x - 1) = 0 \)
   \( x = -9 \) или \( x = 1 \)
7. \( x^2 = 16 \)
   \( x = \pm\sqrt{16} \)
   \( x = \pm 4 \)
8. \( (x - 2) \cdot (-x - 1) = 0 \)
   \( x - 2 = 0 \) или \( -x - 1 = 0 \)
   \( x = 2 \) или \( x = -1 \)
9. \( 7x^2 - 14x = 0 \)
   \( 7x(x - 2) = 0 \)
   \( x = 0 \) или \( x = 2 \)
10. \( 2x^2 + 5x - 3 = 0 \)
    \( D = 5^2 - 4(2)(-3) = 25 + 24 = 49 \)
    \( x = \frac{-5 \pm \sqrt{49}}{2 \cdot 2} = \frac{-5 \pm 7}{4} \)
    \( x_1 = \frac{-5 + 7}{4} = \frac{2}{4} = 0.5 \), \( x_2 = \frac{-5 - 7}{4} = \frac{-12}{4} = -3 \)
11. \( 4x^2 + 21 = 0 \)
    \( 4x^2 = -21 \)
    \( x^2 = -\frac{21}{4} \)
    Действительных корней нет.
12. \( 3x^2 - 2x + 4 = 0 \)
    \( D = (-2)^2 - 4(3)(4) = 4 - 48 = -44 \)
    Действительных корней нет.

Ответ: 1. \( x = \pm 7 \); 2. \( x = 0, x = 8 \); 3. \( x = 5 \); 4. \( x = \pm 13 \); 5. \( x = 0, x = 3 \); 6. \( x = -9, x = 1 \); 7. \( x = \pm 4 \); 8. \( x = 2, x = -1 \); 9. \( x = 0, x = 2 \); 10. \( x = 0.5, x = -3 \); 11. Действительных корней нет; 12. Действительных корней нет.