Question

Solve the following quadratic equation using square roots: (x+6)22=8
.(1 point)
Responses

{−2,−10}
left brace negative 2 comma negative 10 right brace

{10,−22}
left brace 10 comma negative 22 right brace

​ {−0.34,−11.66}
​ left brace negative 0.34 comma negative 11.66 right brace

{−1.17,−6.83}
left brace negative 1.17 comma negative 6.83 right brace

Answer 1

To solve the quadratic equation \((x + 6)^2 = 8\) using square roots, follow these steps:

1. **Take the square root of both sides**:
\[
x + 6 = \pm \sqrt{8}
\]

2. **Simplify \(\sqrt{8}\)**:
\[
\sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}
\]
Thus, we have:
\[
x + 6 = 2\sqrt{2} \quad \text{or} \quad x + 6 = -2\sqrt{2}
\]

3. **Solve for \(x\)** in each case:

- For \(x + 6 = 2\sqrt{2}\):
\[
x = 2\sqrt{2} - 6
\]

- For \(x + 6 = -2\sqrt{2}\):
\[
x = -2\sqrt{2} - 6
\]

4. **Find the approximate values**:
- For \(x = 2\sqrt{2} - 6\):
\[
2 \sqrt{2} \approx 2 \times 1.414 \approx 2.828
\]
Therefore:
\[
x \approx 2.828 - 6 \approx -3.172
\]

- For \(x = -2\sqrt{2} - 6\):
\[
-2\sqrt{2} \approx -2.828
\]
So:
\[
x \approx -2.828 - 6 \approx -8.828
\]

Thus, the approximate solutions are:
\[
{x} \approx \{-3.172, -8.828\}
\]

However, none of these solutions match the options provided.

Let’s re-evaluate and double-check the original quadratic equation provided in the responses for any possible mistakes:

Given the provided options:
- {−2,−10}
- {10,−22}
- {−0.34,−11.66}
- {−1.17,−6.83}

### Finding the correct solutions:
But without any further context on the original question, we can cross-check.
By considering our derived equations or possibly backtracking into the original equation if it's solvable:

Returning to our derived equations:
- \(x = -2\sqrt{2} - 6 \approx -8.828\) is more than likely wrapping up into a non-integer solution.

### Conclusion:
The option that closely could fit based on any scheduling rounding towards integer tries is:
Thus if the option resolves to what we expect if we delegate thoroughly once more (i.e., integers among outputs):
This alludes that approaching into the \{-2, -10\} is plausible here only through converging or other acceptance.

Final recourse without technical disqualification aside looks to yield towards:
Hence we can conclude:
**The closest response for feasible checking potentially leads up to {-2, -10}.**