Solve the following equations: LB: 1. x^2 = 49 2. x^2 - 8x = 0 3. x^2 - 10x + 25 = 0 4. x^2 - 169 = 0 5. x^2 = 3x 6. x^2 + 8x = 9 7. x^2 = 16 8. (x-2) * (-x-1) = 0 9. 7x^2 - 14x = 0 10. 2x^2 + 5x - 3 = 0 11. 4x^2 + 21 = 0 12. 3x^2 - 2x + 4 = 0 II B: 1. x^2 = 64 2. x^2 + 8x = 0 3. x^2 + 8x + 16 = 0 4. x^2 = 225 5. x^2 = 8x 6. x^2 = 5x - 6 7. x^2 - 4 = 0 8. (x-1) * (-x-4) = 0 9. 4x^2 - 20x = 0 10. 2x^2 - 9x - 5 = 0 11. x^2 + 16 = 0 12. x^2 - 4x + 16 = 0

LB:

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

II B:

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