Question

Solve the following quadratic equation using square roots: −9+(x−3)2−4=−4
(1 point)
Responses

{2, -8}
{2, -8}

{8, -2}
{8, -2}

{16, -10}

Answer 1

To solve the equation \( -9 + (x - 3)^2 - 4 = -4 \), we can first simplify it:

1. Combine the constants on the left side:
\[
-9 - 4 = -13
\]
The equation now looks like this:
\[
(x - 3)^2 - 13 = -4
\]

2. Add \( 13 \) to both sides to isolate the squared term:
\[
(x - 3)^2 = -4 + 13
\]
\[
(x - 3)^2 = 9
\]

3. Now take the square root of both sides:
\[
x - 3 = \pm 3
\]

4. Solve for \( x \) in both cases:

- Case 1:
\[
x - 3 = 3 \implies x = 6
\]

- Case 2:
\[
x - 3 = -3 \implies x = 0
\]

So the solutions to the quadratic equation are \( x = 6 \) and \( x = 0 \).

Now let's represent these results as a set:

The solutions are \( \{6, 0\} \).

None of the provided responses seem to match our results directly. Please check if there was an error either in the equation or the answer choices.