Question

2 (2x+1)^2-(2x-2)(2x+2)=17

Answer 1

Качество не очень, но зато решение есть

Answer 2

To solve the equation 2(2x+1)^2 - (2x-2)(2x+2) = 17, you can follow these steps:

1. Expand and simplify both sides of the equation:

   Start with the left side: 2(2x+1)^2 - (2x-2)(2x+2)

   Expand the square: 2(4x^2 + 4x + 1) - (4x^2 - 4)

   Distribute the 2 on the left side: 8x^2 + 8x + 2 - (4x^2 - 4)

   Remove the parentheses on the right side by changing the signs inside the second term: 8x^2 + 8x + 2 - 4x^2 + 4

   Combine like terms: 4x^2 + 8x + 2 - 4

   Simplify further: 4x^2 + 8x - 2

2. Now, rewrite the equation with the simplified left side:

   4x^2 + 8x - 2 = 17

3. Move 17 to the other side of the equation by subtracting it from both sides:

   4x^2 + 8x - 2 - 17 = 0

4. Combine like terms:

   4x^2 + 8x - 19 = 0

5. Now, you have a quadratic equation in the form ax^2 + bx + c = 0, where a = 4, b = 8, and c = -19.

6. You can solve this quadratic equation using the quadratic formula:

   x = (-b ± √(b^2 - 4ac)) / (2a)

   Plugging in the values: x = (-8 ± √(8^2 - 4 * 4 * (-19))) / (2 * 4)

   x = (-8 ± √(64 + 304)) / 8

   x = (-8 ± √368) / 8

7. Further simplify the square root:

   x = (-8 ± 4√23) / 8

8. Factor out a common factor of 4 in the numerator:

   x = (4(-2 ± √23)) / 8

9. Simplify the fraction by canceling a common factor of 4:

   x = (-2 ± √23) / 2

So, the solutions to the equation are:

x₁ = (-2 + √23) / 2 x₂ = (-2 - √23) / 2