Question

Solve the following quadratic equation using square roots: (x−7)2−94=0
.(1 point)
Responses

{−4,−10}
left brace negative 4 comma negative 10 right brace

{10,4}
left brace 10 comma 4 right brace

{10.61,3.39}
left brace 10.61 comma 3.39 right brace

{2,−16}

Answer 1

To solve the quadratic equation \((x - 7)^2 - 94 = 0\) using square roots, we follow these steps:

1. **Isolate the square**:
\[
(x - 7)^2 = 94
\]

2. **Take the square root of both sides**:
\[
x - 7 = \pm \sqrt{94}
\]

3. **Solve for \(x\)**:
\[
x = 7 \pm \sqrt{94}
\]

Now we evaluate \(\sqrt{94}\). It is approximately \(9.70\).

So, we have two solutions:
1. \(x = 7 + \sqrt{94} \approx 7 + 9.70 \approx 16.70\)
2. \(x = 7 - \sqrt{94} \approx 7 - 9.70 \approx -2.70\)

Neither of these values appear directly in the provided options. Let's estimate \(\sqrt{94}\) more accurately:

Since \(\sqrt{94} \approx 9.695\),
- \(x_1 \approx 7 + 9.695 \approx 16.695 \approx 16.7\)
- \(x_2 \approx 7 - 9.695 \approx -2.695\)

It seems based on provided options, we made calculation errors or the values might not match closely. However, in terms of rational justification for closer approximations, let's choose between the computed values or select logical pairs.

None of the provided options in the set that include values suggest proximity to our approximations, so we can conclude the initial approaches did fall short.

### Final Answer:
Since none of the options provided correspond closely with correct computations or straightforward rationales, we can conclude that our output isn't precisely among listed.

This symbolically depicts that the correct results would have been reliant on approximated evaluation through traditional rationalization, differing outputs from provided selections had we continued solving.