Question

(2x+3)(4x-3)-2x(4x+1)-17=7​

Answer 1

(2x + 3) (4x - 3) - 2x (4x + 1) - 17 = 7​

8х² - 6х + 12х - 9 - 8х² - 2х - 17 = 7

4х - 26 = 7

4х = 7 + 26

4х = 33

х = $\frac{33}{4}$

Answer 2

To solve the equation (2x + 3)(4x - 3) - 2x(4x + 1) - 17 = 7, follow these steps:

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

(2x + 3)(4x - 3) - 2x(4x + 1) - 17 = 7

Expanding the left side: (2x)(4x) + (2x)(-3) + (3)(4x) + (3)(-3) - 2x(4x) - 2x(1) - 17 = 7

8x^2 - 6x + 12x - 9 - 8x - 2x - 17 = 7

2. Combine like terms on the left side of the equation:

8x^2 + (12x - 8x - 2x) - 6x - 9 - 17 = 7

8x^2 + 2x - 6x - 9 - 17 = 7

3. Simplify further:

8x^2 - 4x - 26 = 7

4. Move 7 to the right side by subtracting it from both sides of the equation:

8x^2 - 4x - 26 - 7 = 0

8x^2 - 4x - 33 = 0

5. Now, you have a quadratic equation in the form ax^2 + bx + c = 0, where a = 8, b = -4, and c = -33.

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

x = (-b ± √(b² - 4ac)) / (2a)

Plugging in the values:

x = (-(-4) ± √((-4)² - 4(8)(-33))) / (2(8))

x = (4 ± √(16 + 1056)) / 16

x = (4 ± √1072) / 16

x = (4 ± √(16 * 67)) / 16

x = (4 ± 4√67) / 16

x = (1 ± √67) / 4

So, the solutions to the equation are:

x = (1 + √67) / 4 and x = (1 - √67) / 4