Question

4+x=-x√(1-(8/(9x+8))

Answer 1

Ответ:

$x1 = - \frac{8}{5} \: \: \: x2 = - 1$

Answer 2

To solve the equation 4 + x = -x√(1 - 8/(9x + 8)), we'll need to isolate the variable on one side of the equation. Let's go through the steps:

1. Start by squaring both sides of the equation to eliminate the square root: (4 + x)^2 = (-x√(1 - 8/(9x + 8)))^2

2. Simplify the equation: 16 + 8x + x^2 = x^2(1 - 8/(9x + 8))

3. Expand and simplify: 16 + 8x + x^2 = x^2 - 8x^2/(9x + 8)

4. Move all the terms to one side of the equation: 16 + 8x + x^2 - x^2 + 8x^2/(9x + 8) = 0

5. Combine like terms: 16 + 16x + 8x^2/(9x + 8) = 0

6. Multiply through by (9x + 8) to eliminate the fraction: (9x + 8)(16 + 16x + 8x^2/(9x + 8)) = 0

7. Expand and simplify: 144x + 128 + 144x^2 + 128x^2 = 0

8. Combine like terms: 272x + 272x^2 + 128 = 0

9. Rearrange the equation: 272x^2 + 272x + 128 = 0

At this point, we have a quadratic equation in standard form. We can solve it using the quadratic formula or factoring. However, upon closer inspection, we can see that the quadratic equation does not factor easily. Therefore, let's use the quadratic formula to find the solutions:

x = (-b ± √(b^2 - 4ac)) / (2a)

In our equation, a = 272, b = 272, and c = 128. Plugging these values into the quadratic formula, we get:

x = (-272 ± √(272^2 - 4 * 272 * 128)) / (2 * 272)

Simplifying further:

x = (-272 ± √(73984 - 139264)) / 544

x = (-272 ± √(-65280)) / 544

Since the value under the square root is negative, the equation has no real solutions. The equation is not satisfied for any real value of x.