Question

(2r+3)(4х-3)-rx²=2x-17?

Answer 1

(2r+3)×(4x-3)-rx²×2x-17=8rx-6r+12x-9-2rx³-17=8rx-6r+12x-26-2rx³

Answer 2

To solve the equation (2r + 3)(4x - 3) - rx^2 = 2x - 17, you can follow these steps:

1. First, distribute the terms within the parentheses:

   8rx - 6r + 12x - 9 - rx^2 = 2x - 17

2. Rearrange the equation by moving all terms to one side to set it equal to zero:

   8rx + 12x - rx^2 - 6r - 9 - 2x + 17 = 0

3. Combine like terms:

   8rx - rx^2 + 12x - 2x - 6r - 9 + 17 = 0

4. Further simplify the equation:

   8rx - rx^2 + 10x - 6r + 8 = 0

5. This is a quadratic equation in terms of x. To solve for x, you can use the quadratic formula:

   x = (-B ± √(B^2 - 4AC)) / (2A)

   In this case, A = -r, B = 10, and C = 8r - 6r + 8 = 2r + 8.

   Plug these values into the quadratic formula:

   x = (-10 ± √(10^2 - 4(-r)(2r + 8))) / (2(-r))

6. Now, you can simplify the equation further:

   x = (-10 ± √(100 + 8r^2 + 32r)) / (-2r)

   x = (-10 ± √(100 + 8r^2 + 32r)) / (-2r)

7. You have two potential solutions for x:

   x₁ = (-10 + √(100 + 8r^2 + 32r)) / (-2r) x₂ = (-10 - √(100 + 8r^2 + 32r)) / (-2r)

These are the solutions for x in terms of r. Please note that the solutions may vary depending on the specific values of r, and you can further simplify the expressions if needed.