Question

32.27. 1) (7 - 8x)(2x + 1) + (4x - 1)2 = 0; 2) (2x - 5)2 - (2x - 3)(2x + 3) = 15; 3) (3x + 5)(3x - 5) -(3x - 1)2 = -4; 4) (9x + 2)(1 - 4x ) + (5 - 6x)2 = -32. ​

Answer 1

Надеюсь это то что надо было сделать

Answer 2

Let's solve each of the given equations one by one:

1. (7 - 8x)(2x + 1) + (4x - 1)2 = 0

Expanding the equation, we have:

(14x^2 + 7x - 16x - 8) + (16x^2 - 8x - 8) = 0

Combine like terms:

30x^2 - 17x - 16 = 0

Now we can solve this quadratic equation. We can either factor it or use the quadratic formula. In this case, factoring is not straightforward, so we'll use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 30, b = -17, and c = -16. Substituting these values into the formula, we have:

x = (-(-17) ± √((-17)^2 - 4 * 30 * -16)) / (2 * 30)

Simplifying further:

x = (17 ± √(289 + 1920)) / 60

x = (17 ± √2209) / 60

x = (17 ± 47) / 60

There are two possible solutions:

x1 = (17 + 47) / 60 = 64 / 60 = 32 / 30 = 16 / 15 x2 = (17 - 47) / 60 = -30 / 60 = -1 / 2

Therefore, the solutions to the first equation are x = 16/15 and x = -1/2.

2. (2x - 5)2 - (2x - 3)(2x + 3) = 15

Expanding the equation, we have:

(4x^2 - 20x + 25) - (4x^2 - 9) = 15

Simplifying further:

-20x + 25 + 9 = 15

-20x + 34 = 15

-20x = 15 - 34

-20x = -19

Dividing both sides by -20:

x = -19 / -20

x = 19 / 20

Therefore, the solution to the second equation is x = 19/20.

3. (3x + 5)(3x - 5) - (3x - 1)2 = -4

Expanding the equation, we have:

(9x^2 - 25) - (9x^2 - 6x + 1) = -4

Simplifying further:

-25 + 6x - 1 = -4

6x - 26 = -4

6x = -4 + 26

6x = 22

Dividing both sides by 6:

x = 22 / 6

Simplifying further:

x = 11 / 3

Therefore, the solution to the third equation is x = 11/3.

4. (9x + 2)(1 - 4x) + (5 - 6x)2 = -32

Expanding the equation, we have:

(9x - 36x^2 + 2 - 8x) + (25 - 60x + 36x^2) = -32

Combine like terms:

-36x^2 + 9x - 36x^2 - 8x + 36x^2 + 36x^2 - 60x + 25