1) (x - 2) (2x+3)-05x = 3 + 2x2 2) x (3x + 2) - (x + 1) (3x - 2) = 4x + 3 3) 2 (3x - 1) + (2x – 3) (2x + 5) = 4x2 – 3x + 9 4) (3x + 7) - (x + 6) (x - 5) = 7 - x2 5) 5x (7 + x) - (4x - 7) = 5x² - (6x + 13) 6) 3x (x + 4) - (3x – 1) (x + 6) = 13 - 6x 7) 5 (4x - 9) + 2 (x - 3) (x + 5) = 4 + 2x2 8) 9-(3x-2)(x - 8) = 4x - x (3x - 9) + 12 9) 9x (2x + 4) – (x - 3) (18x + 3) = 4 -9x 10) 4x - 6x (2x + 3) = 9 - (3x+4) (4x + 3) 11) 9 (5x + 2) – x (5x + 4) = 12 – 5x2 12) 2 (x – 6) (3 - x) + 12 = 9 – 2x (x + 5) 13) (9 -2x) (x+2) - (3x + 2) = 9 – 2x2 14) 2x - x (x + 3) (4 – x) = x (x² - 8) + 11 15) 5x (2x + 3) - (2x+1) (5x-6) = 3 - 4 (x + 2) 16) 4 (x2 – 3) = 4x (x + 5) – 14 17) (6x – 1) (6x+1) – 12x (3x + 2) = 11x - 8 18) (3x + 2) (x – 1) – 3 = 7 + 3x (x + 4)

Давай решим уравнения по порядку! 1) \[(x - 2) (2x+3)-0.5x = 3 + 2x^2\] \[2x^2 + 3x - 4x - 6 - 0.5x = 3 + 2x^2\] \[-x - 0.5x = 9\] \[-1.5x = 9\] \[x = -6\]

Ответ: x = -6

2) \[x (3x + 2) - (x + 1) (3x - 2) = 4x + 3\] \[3x^2 + 2x - (3x^2 - 2x + 3x - 2) = 4x + 3\] \[3x^2 + 2x - 3x^2 + 2x - 3x + 2 = 4x + 3\] \[x = 1\]

Ответ: x = 1

3) \[2 (3x - 1) + (2x – 3) (2x + 5) = 4x^2 – 3x + 9\] \[6x - 2 + 4x^2 + 10x - 6x - 15 = 4x^2 – 3x + 9\] \[10x - 17 = -3x + 9\] \[13x = 26\] \[x = 2\]

Ответ: x = 2

4) \[(3x + 7) - (x + 6) (x - 5) = 7 - x^2\] \[3x + 7 - (x^2 - 5x + 6x - 30) = 7 - x^2\] \[3x + 7 - x^2 + 5x - 6x + 30 = 7 - x^2\] \[2x + 30 = 0\] \[x = -15\]

Ответ: x = -15

5) \[5x (7 + x) - (4x - 7) = 5x^2 - (6x + 13)\] \[35x + 5x^2 - 4x + 7 = 5x^2 - 6x - 13\] \[31x + 7 = -6x - 13\] \[37x = -20\] \[x = -\frac{20}{37}\]

Ответ: x = -20/37

6) \[3x (x + 4) - (3x – 1) (x + 6) = 13 - 6x\] \[3x^2 + 12x - (3x^2 + 18x - x - 6) = 13 - 6x\] \[3x^2 + 12x - 3x^2 - 17x + 6 = 13 - 6x\] \[-5x + 6 = 13 - 6x\] \[x = 7\]

Ответ: x = 7

7) \[5 (4x - 9) + 2 (x - 3) (x + 5) = 4 + 2x^2\] \[20x - 45 + 2 (x^2 + 5x - 3x - 15) = 4 + 2x^2\] \[20x - 45 + 2x^2 + 4x - 30 = 4 + 2x^2\] \[24x - 75 = 4\] \[24x = 79\] \[x = \frac{79}{24}\]

Ответ: x = 79/24

8) \[9-(3x-2)(x - 8) = 4x - x (3x - 9) + 12\] \[9 - (3x^2 - 24x - 2x + 16) = 4x - 3x^2 + 9x + 12\] \[9 - 3x^2 + 26x - 16 = 13x - 3x^2 + 12\] \[26x - 7 = 13x + 12\] \[13x = 19\] \[x = \frac{19}{13}\]

Ответ: x = 19/13

9) \[9x (2x + 4) – (x - 3) (18x + 3) = 4 -9x\] \[18x^2 + 36x - (18x^2 + 3x - 54x - 9) = 4 - 9x\] \[18x^2 + 36x - 18x^2 + 51x + 9 = 4 - 9x\] \[87x + 9 = 4 - 9x\] \[96x = -5\] \[x = -\frac{5}{96}\]

Ответ: x = -5/96

10) \[4x - 6x (2x + 3) = 9 - (3x+4) (4x + 3)\] \[4x - 12x^2 - 18x = 9 - (12x^2 + 9x + 16x + 12)\] \[-12x^2 - 14x = 9 - 12x^2 - 25x - 12\] \[-14x = -25x - 3\] \[11x = -3\] \[x = -\frac{3}{11}\]

Ответ: x = -3/11

11) \[9 (5x + 2) – x (5x + 4) = 12 – 5x^2\] \[45x + 18 - 5x^2 - 4x = 12 - 5x^2\] \[41x + 18 = 12\] \[41x = -6\] \[x = -\frac{6}{41}\]

Ответ: x = -6/41

12) \[2 (x – 6) (3 - x) + 12 = 9 – 2x (x + 5)\] \[2 (3x - x^2 - 18 + 6x) + 12 = 9 - 2x^2 - 10x\] \[6x - 2x^2 - 36 + 12x + 12 = 9 - 2x^2 - 10x\] \[-2x^2 + 18x - 24 = 9 - 2x^2 - 10x\] \[18x - 24 = 9 - 10x\] \[28x = 33\] \[x = \frac{33}{28}\]

Ответ: x = 33/28

13) \[(9 -2x) (x+2) - (3x + 2) = 9 – 2x^2\] \[9x + 18 - 2x^2 - 4x - 3x - 2 = 9 - 2x^2\] \[-2x^2 + 2x + 16 = 9 - 2x^2\] \[2x = -7\] \[x = -\frac{7}{2}\]

Ответ: x = -7/2

14) \[2x - x (x + 3) (4 – x) = x (x² - 8) + 11\] \[2x - x (4x - x^2 + 12 - 3x) = x^3 - 8x + 11\] \[2x - 4x^2 + x^3 - 12x + 3x^2 = x^3 - 8x + 11\] \[x^3 - x^2 - 10x = x^3 - 8x + 11\] \[-x^2 - 2x - 11 = 0\] \[x^2 + 2x + 11 = 0\] \[D = 4 - 44 = -40\]

Ответ: Нет решения, так как дискриминант отрицательный.

15) \[5x (2x + 3) - (2x+1) (5x-6) = 3 - 4 (x + 2)\] \[10x^2 + 15x - (10x^2 - 12x + 5x - 6) = 3 - 4x - 8\] \[10x^2 + 15x - 10x^2 + 7x + 6 = -4x - 5\] \[22x + 6 = -4x - 5\] \[26x = -11\] \[x = -\frac{11}{26}\]

Ответ: x = -11/26

16) \[4 (x^2 – 3) = 4x (x + 5) – 14\] \[4x^2 - 12 = 4x^2 + 20x - 14\] \[-12 = 20x - 14\] \[20x = 2\] \[x = \frac{1}{10}\]

Ответ: x = 1/10

17) \[(6x – 1) (6x+1) – 12x (3x + 2) = 11x - 8\] \[36x^2 - 1 - 36x^2 - 24x = 11x - 8\] \[-24x - 1 = 11x - 8\] \[-35x = -7\] \[x = \frac{1}{5}\]

Ответ: x = 1/5

18) \[(3x + 2) (x – 1) – 3 = 7 + 3x (x + 4)\] \[3x^2 - 3x + 2x - 2 - 3 = 7 + 3x^2 + 12x\] \[3x^2 - x - 5 = 7 + 3x^2 + 12x\] \[-x - 5 = 7 + 12x\] \[-13x = 12\] \[x = -\frac{12}{13}\]

Ответ: x = -12/13

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