Question

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}

{28, -22}
{28, -22}

{16, -10}

Answer 1

To solve the equation \(-9 + (x - 3)^2 - 4 = -4\), let's start simplifying it step by step.

1. Combine the constant terms on the left side:
\[
-9 - 4 = -13
\]
So the equation becomes:
\[
(x - 3)^2 - 13 = -4
\]

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

3. Now take the square root of both sides:
\[
x - 3 = 3 \quad \text{or} \quad x - 3 = -3
\]

4. Solving the first equation:
\[
x - 3 = 3 \implies x = 6
\]

5. Solving the second equation:
\[
x - 3 = -3 \implies x = 0
\]

Now, we have the solutions:
\[
x = 6 \quad \text{and} \quad x = 0
\]

Since neither of the given answer choices match \(6\) and \(0\), let's review and solve the equation again, ensuring all calculations are correct.

Starting again from:
\[
-9 + (x - 3)^2 - 4 = -4
\]
Rearranged:
\[
(x - 3)^2 = 9
\]
Taking the square root gives solutions:
\[
x = 6 \quad \text{and} \quad x = 0
\]

Given this, the response options don't reflect the correct solutions. Please check whether there is any missing information or errors in the answer choices provided.