Solve the quadratic equ -8 $$ x^{2}-6 x-2=0 $$

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UpStudy AI · Accepted Answer

To solve the quadratic equation:

$$
x^{2} - 6x - 2 = 0
$$

we can use the **quadratic formula**, which is:

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

For the given equation, the coefficients are:

- $$ a = 1 $$
- $$ b = -6 $$
- $$ c = -2 $$

**Step 1: Calculate the Discriminant ($$ \Delta $$)**

$$
\Delta = b^2 - 4ac = (-6)^2 - 4(1)(-2) = 36 + 8 = 44
$$

**Step 2: Apply the Quadratic Formula**

$$
x = \frac{-(-6) \pm \sqrt{44}}{2 \times 1} = \frac{6 \pm \sqrt{44}}{2}
$$

Simplify $$ \sqrt{44} $$:

$$
\sqrt{44} = \sqrt{4 \times 11} = 2\sqrt{11}
$$

So,

$$
x = \frac{6 \pm 2\sqrt{11}}{2} = 3 \pm \sqrt{11}
$$

**Solutions:**

$$
x = 3 + \sqrt{11} \quad \text{and} \quad x = 3 - \sqrt{11}
$$

**Approximate Values:**

- $$ \sqrt{11} \approx 3.3166 $$
- $$ x \approx 3 + 3.3166 = 6.3166 $$
- $$ x \approx 3 - 3.3166 = -0.3166 $$

**Final Answer:**

$$
x = 3 + \sqrt{11} \quad \text{and} \quad x = 3 - \sqrt{11}
$$
The solutions to the equation $$ x^{2} - 6x - 2 = 0 $$ are $$ x = 3 + \sqrt{11} $$ and $$ x = 3 - \sqrt{11} $$.

Solve the quadratic equ
-8

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