Question

Solve the following quadratic equation using square roots:

−9+(x−3)^2/−4 = −4
(1 point)
Responses

{28,−22}
start set 28 comma negative 22 end set

{8,−2}
start set 8 comma negative 2 end set

{16,−10}
start set 16 comma negative 10 end set

{2,−8}

Answer 1

pick one listed

Answer 2

To solve the given quadratic equation

\[
-\frac{9 + (x - 3)^2}{-4} = -4,
\]

we can first simplify it. Multiplying both sides by -4 to eliminate the negative sign gives:

\[
9 + (x - 3)^2 = 16.
\]

Next, we can isolate \((x - 3)^2\):

\[
(x - 3)^2 = 16 - 9,
\]
\[
(x - 3)^2 = 7.
\]

Now, we take the square root of both sides:

\[
x - 3 = \pm \sqrt{7}.
\]

This results in two equations:

1. \(x - 3 = \sqrt{7}\)
2. \(x - 3 = -\sqrt{7}\)

Solving these gives:

1. \(x = 3 + \sqrt{7}\)
2. \(x = 3 - \sqrt{7}\)

Approximating \(\sqrt{7} \approx 2.646\):

1. \(x \approx 3 + 2.646 \approx 5.646\)
2. \(x \approx 3 - 2.646 \approx 0.354\)

Since these do not map directly to any of the response options, it's important to check the exact values. Therefore, the exact solutions are:

\[
x = 3 + \sqrt{7}, \quad x = 3 - \sqrt{7}.
\]

The roots do not match any provided sets.

You may want to check the math again or review the options given, as none align. If you're specifically looking for integer approximations or squared terms, they may not produce exact integers as seen in standard set options given.

If just matching to the set of integers, the most logical approximation to choose from those sets would be the closest matches to \(5.646\) and \(0.354\) if done in a general sense, however, exact solutions should be noted as above.

Therefore, if needing specific set values or further interpret values, let me know how you'd like to proceed!

Answer 3

Based on the previous calculations, the approximate solutions were:

1. \(x \approx 5.646\)
2. \(x \approx 0.354\)

Given the response options:

- {28, −22}
- {8, −2}
- {16, −10}
- {2, −8}

The closest integers to our approximations of \(5.646\) and \(0.354\) could be seen as {8, −2}.

So, I would choose:

**{8, −2}**.