Solve the quadratic equations.

Решение:

1. Уравнение 10: \( x^2 - 5.6x + 6.4 = 0 \)
   \( D = (-5.6)^2 - 4 \cdot 1 \cdot 6.4 = 31.36 - 25.6 = 5.76 \)
   \( \sqrt{D} = 2.4 \)
   \( x_1 = \frac{5.6 + 2.4}{2} = \frac{8}{2} = 4 \)
   \( x_2 = \frac{5.6 - 2.4}{2} = \frac{3.2}{2} = 1.6 \)
2. Уравнение 11: \( x^2 + 2.5x + 1 = 0 \)
   \( D = (2.5)^2 - 4 \cdot 1 \cdot 1 = 6.25 - 4 = 2.25 \)
   \( \sqrt{D} = 1.5 \)
   \( x_1 = \frac{-2.5 + 1.5}{2} = \frac{-1}{2} = -0.5 \)
   \( x_2 = \frac{-2.5 - 1.5}{2} = \frac{-4}{2} = -2 \)
3. Уравнение 12: \( x^2 - 4.5x + 4.5 = 0 \)
   \( D = (-4.5)^2 - 4 \cdot 1 \cdot 4.5 = 20.25 - 18 = 2.25 \)
   \( \sqrt{D} = 1.5 \)
   \( x_1 = \frac{4.5 + 1.5}{2} = \frac{6}{2} = 3 \)
   \( x_2 = \frac{4.5 - 1.5}{2} = \frac{3}{2} = 1.5 \)
4. Уравнение 13: \( -x^2 + 2x + 8 = 0 \)
   \( x^2 - 2x - 8 = 0 \)
   \( D = (-2)^2 - 4 \cdot 1 \cdot (-8) = 4 + 32 = 36 \)
   \( \sqrt{D} = 6 \)
   \( x_1 = \frac{2 + 6}{2} = \frac{8}{2} = 4 \)
   \( x_2 = \frac{2 - 6}{2} = \frac{-4}{2} = -2 \)
5. Уравнение 14: \( -x^2 + 7x - 10 = 0 \)
   \( x^2 - 7x + 10 = 0 \)
   \( D = (-7)^2 - 4 \cdot 1 \cdot 10 = 49 - 40 = 9 \)
   \( \sqrt{D} = 3 \)
   \( x_1 = \frac{7 + 3}{2} = \frac{10}{2} = 5 \)
   \( x_2 = \frac{7 - 3}{2} = \frac{4}{2} = 2 \)
6. Уравнение 15: \( -x^2 + 7x + 8 = 0 \)
   \( x^2 - 7x - 8 = 0 \)
   \( D = (-7)^2 - 4 \cdot 1 \cdot (-8) = 49 + 32 = 81 \)
   \( \sqrt{D} = 9 \)
   \( x_1 = \frac{7 + 9}{2} = \frac{16}{2} = 8 \)
   \( x_2 = \frac{7 - 9}{2} = \frac{-2}{2} = -1 \)
7. Уравнение 16: \( -x^2 - 2x + 15 = 0 \)
   \( x^2 + 2x - 15 = 0 \)
   \( D = 2^2 - 4 \cdot 1 \cdot (-15) = 4 + 60 = 64 \)
   \( \sqrt{D} = 8 \)
   \( x_1 = \frac{-2 + 8}{2} = \frac{6}{2} = 3 \)
   \( x_2 = \frac{-2 - 8}{2} = \frac{-10}{2} = -5 \)
8. Уравнение 17: \( 3x^2 - 5x - 2 = 0 \)
   \( D = (-5)^2 - 4 \cdot 3 \cdot (-2) = 25 + 24 = 49 \)
   \( \sqrt{D} = 7 \)
   \( x_1 = \frac{5 + 7}{2 \cdot 3} = \frac{12}{6} = 2 \)
   \( x_2 = \frac{5 - 7}{2 \cdot 3} = \frac{-2}{6} = -\frac{1}{3} \)
9. Уравнение 18: \( 4x^2 + x - 3 = 0 \)
   \( D = 1^2 - 4 \cdot 4 \cdot (-3) = 1 + 48 = 49 \)
   \( \sqrt{D} = 7 \)
   \( x_1 = \frac{-1 + 7}{2 \cdot 4} = \frac{6}{8} = \frac{3}{4} \)
   \( x_2 = \frac{-1 - 7}{2 \cdot 4} = \frac{-8}{8} = -1 \)
10. Уравнение 19: \( 2x^2 - 7x + 6 = 0 \)
    \( D = (-7)^2 - 4 \cdot 2 \cdot 6 = 49 - 48 = 1 \)
    \( \sqrt{D} = 1 \)
    \( x_1 = \frac{7 + 1}{2 \cdot 2} = \frac{8}{4} = 2 \)
    \( x_2 = \frac{7 - 1}{2 \cdot 2} = \frac{6}{4} = \frac{3}{2} \)
11. Уравнение 20: \( 5x^2 - 8x + 3 = 0 \)
    \( D = (-8)^2 - 4 \cdot 5 \cdot 3 = 64 - 60 = 4 \)
    \( \sqrt{D} = 2 \)
    \( x_1 = \frac{8 + 2}{2 \cdot 5} = \frac{10}{10} = 1 \)
    \( x_2 = \frac{8 - 2}{2 \cdot 5} = \frac{6}{10} = \frac{3}{5} \)
12. Уравнение 21: \( 10x^2 - 3x - 1 = 0 \)
    \( D = (-3)^2 - 4 \cdot 10 \cdot (-1) = 9 + 40 = 49 \)
    \( \sqrt{D} = 7 \)
    \( x_1 = \frac{3 + 7}{2 \cdot 10} = \frac{10}{20} = \frac{1}{2} \)
    \( x_2 = \frac{3 - 7}{2 \cdot 10} = \frac{-4}{20} = -\frac{1}{5} \)
13. Уравнение 22: \( 3x^2 + 11x + 6 = 0 \)
    \( D = 11^2 - 4 \cdot 3 \cdot 6 = 121 - 72 = 49 \)
    \( \sqrt{D} = 7 \)
    \( x_1 = \frac{-11 + 7}{2 \cdot 3} = \frac{-4}{6} = -\frac{2}{3} \)
    \( x_2 = \frac{-11 - 7}{2 \cdot 3} = \frac{-18}{6} = -3 \)
14. Уравнение 23: \( 3x^2 + 2x - 8 = 0 \)
    \( D = 2^2 - 4 \cdot 3 \cdot (-8) = 4 + 96 = 100 \)
    \( \sqrt{D} = 10 \)
    \( x_1 = \frac{-2 + 10}{2 \cdot 3} = \frac{8}{6} = \frac{4}{3} \)
    \( x_2 = \frac{-2 - 10}{2 \cdot 3} = \frac{-12}{6} = -2 \)
15. Уравнение 24: \( 4x^2 - 17x - 15 = 0 \)
    \( D = (-17)^2 - 4 \cdot 4 \cdot (-15) = 289 + 240 = 529 \)
    \( \sqrt{D} = 23 \)
    \( x_1 = \frac{17 + 23}{2 \cdot 4} = \frac{40}{8} = 5 \)
    \( x_2 = \frac{17 - 23}{2 \cdot 4} = \frac{-6}{8} = -\frac{3}{4} \)
16. Уравнение 25: \( x(x+2) = 3 \)
    \( x^2 + 2x - 3 = 0 \)
    \( D = 2^2 - 4 \cdot 1 \cdot (-3) = 4 + 12 = 16 \)
    \( \sqrt{D} = 4 \)
    \( x_1 = \frac{-2 + 4}{2} = \frac{2}{2} = 1 \)
    \( x_2 = \frac{-2 - 4}{2} = \frac{-6}{2} = -3 \)