Question

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

{2,−8}
left brace 2 comma negative 8 right brace

{8,−2}
left brace 8 comma negative 2 right brace

{16,−10}
left brace 16 comma negative 10 right brace

{28,−22}

Answer 1

To solve the given quadratic equation using square roots, we start by simplifying it. The equation is:

\[
-9 + (x - 3)^2 - 4 = -4
\]

Let's simplify the left side:

1. Combine constants on the left:
\[
-9 - 4 = -13
\]
So we rewrite the equation as:
\[
-13 + (x - 3)^2 = -4
\]

2. Now, add 13 to both sides:
\[
(x - 3)^2 = -4 + 13
\]
\[
(x - 3)^2 = 9
\]

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

4. Now solve for \(x\):
- For the positive case:
\[
x - 3 = 3 \implies x = 6
\]
- For the negative case:
\[
x - 3 = -3 \implies x = 0
\]

Thus, the solutions are \(x = 6\) and \(x = 0\).

Finally, we represent this as a set of solutions:
\[
\{6, 0\}
\]

However, none of the given response options match this answer. There might be a mistake in the options or in the question provided.

Would you like to solve a different problem or clarify anything?