Question

4(x-1)(x-2) - (3+2x)(2x-3)=38​

Answer 1

Ответ:

(4х-4)(х-2)-(2х+3)(2х-3)=32

4х^2-8х+8-(4х^2-9)=32

4х^2-8х-4х+8-4х^2+9=38

-12х+17=38

-12х=38-17

-12х=21

х=7/4

Answer 2

To solve the equation 4(x-1)(x-2) - (3+2x)(2x-3) = 38, follow these steps:

1. Expand the expressions on both sides of the equation:

   4(x-1)(x-2) - (3+2x)(2x-3) = 38

   Expand the first term on the left side: 4(x^2 - 2x - x + 2) - (3+2x)(2x-3) = 38

   Expand the second term on the left side: 4(x^2 - 3x + 2) - (3+2x)(2x-3) = 38

2. Continue expanding the equation:

   4x^2 - 12x + 8 - (3+2x)(2x-3) = 38

3. Distribute the -1 inside the parentheses on the right side:

   4x^2 - 12x + 8 - (6x^2 - 9x + 4x - 6) = 38

4. Remove the parentheses and simplify:

   4x^2 - 12x + 8 - 6x^2 + 9x - 4x + 6 = 38

5. Combine like terms:

   (4x^2 - 6x^2) + (-12x + 9x - 4x) + (8 + 6 - 38) = 0

6. Further simplify:

   -2x^2 - 7x - 24 = 0

7. Rearrange the equation to set it equal to zero:

   -2x^2 - 7x - 24 = 0

8. To solve this quadratic equation, you can use the quadratic formula:

   x = (-b ± √(b² - 4ac)) / (2a)

   In this case, a = -2, b = -7, and c = -24. Plug these values into the formula:

   x = (-(-7) ± √((-7)² - 4(-2)(-24))) / (2(-2))

   x = (7 ± √(49 - 192)) / (-4)

   x = (7 ± √(-143)) / (-4)

Since the discriminant (the value inside the square root) is negative, this equation has complex solutions. You can simplify the expression further:

x = (7 ± √(143)i) / (-4)

So, the solutions for the equation are complex numbers:

x = (7 + √(143)i) / (-4) and x = (7 - √(143)i) / (-4)