Which of the following are the approximate solutions of the quadratic equation $$ x^{2} \quad 9 x-29=07 $$ $$ x=4.5,-2.5 $$ $$ x=11.5,2.5 $$ $$ x=11.5,-2.5 $$ $$ \begin{array}{l}x=3.5,-2.5 \ \ x\end{array} $$

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To solve the quadratic equation $$ x^{2} - 9x - 29 = 0 $$, we'll use the quadratic formula:

$$
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
$$

Here, $$ a = 1 $$, $$ b = -9 $$, and $$ c = -29 $$.

1. **Calculate the discriminant (Δ):**
   $$
   \Delta = b^2 - 4ac = (-9)^2 - 4(1)(-29) = 81 + 116 = 197
   $$

2. **Find the square root of the discriminant:**
   $$
   \sqrt{197} \approx 14.0357
   $$

3. **Apply the quadratic formula:**
   $$
   x = \frac{9 \pm 14.0357}{2}
   $$
   
   - **First solution:**
     $$
     x = \frac{9 + 14.0357}{2} = \frac{23.0357}{2} \approx 11.5179 \approx 11.5
     $$
   
   - **Second solution:**
     $$
     x = \frac{9 - 14.0357}{2} = \frac{-5.0357}{2} \approx -2.5179 \approx -2.5
     $$

**Approximate Solutions:**
$$
x \approx 11.5 \quad \text{and} \quad x \approx -2.5
$$

**Therefore, the correct answer is:**

**$$ x = 11.5,\ -2.5 $$**
The approximate solutions are $$ x = 11.5 $$ and $$ x = -2.5 $$.

Which of the following are the approximate solutions of the quadratic equation \( x^{2} \quad 9 x-29=07 \) \( x=4.5,-2.5 \) \( x=11.5,2.5 \) \( x=11.5,-2.5 \) \( \begin{array}{l}x=3.5,-2.5 \\ \\ x\end{array} \)

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