Question

2) (2x-6)(8x+5)+(3-4x)(3+4x)=55

Answer 1

Ответ:

решение смотри на фотографии

Пошаговое объяснение:

Answer 2

To solve the equation (2x-6)(8x+5)+(3-4x)(3+4x)=55, you can start by expanding and simplifying both sides of the equation. Here's the step-by-step solution:

1. Start by expanding both sets of parentheses:

(2x-6)(8x+5) + (3-4x)(3+4x) = 55

Expanding the first set of parentheses:

(2x)(8x) + (2x)(5) + (-6)(8x) + (-6)(5) + (3-4x)(3+4x) = 55

Now, simplify each term:

16x^2 + 10x - 48x - 30 + (3-4x)(3+4x) = 55

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

(16x^2 - 48x) + (10x - 30) + (3-4x)(3+4x) = 55

Now, simplify further:

16x^2 - 38x - 30 + (3-4x)(3+4x) = 55

3. Move all terms to one side of the equation to set it equal to zero:

16x^2 - 38x - 30 + (3-4x)(3+4x) - 55 = 0

4. Combine the constants:

16x^2 - 38x - 30 - 52x^2 = 0

5. Combine like terms:

-36x^2 - 38x - 30 - 52x^2 = 0

-88x^2 - 38x - 30 = 0

6. Now, you have a quadratic equation in the form of ax^2 + bx + c = 0, where a = -88, b = -38, and c = -30.

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

x = (-b ± √(b² - 4ac)) / (2a)

Plugging in the values:

x = (-(-38) ± √((-38)² - 4(-88)(-30))) / (2(-88))

x = (38 ± √(1444 - 10560)) / (-176)

Now, calculate the discriminant (the value inside the square root):

Discriminant = 1444 - 10560 = -9116

Since the discriminant is negative, there are no real solutions to this quadratic equation. The equation does not have real roots.

So, the solution to the equation (2x-6)(8x+5)+(3-4x)(3+4x)=55 is that it has no real solutions.