Question

Solve the following quadratic equation using square roots:

−9+(x−3)2−4=−4


(1 point)
Responses

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

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

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

{16,−10}

Answer 1

To solve the equation:

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

we can first simplify the left side:

\[
-9 - 4 + (x - 3)^2 = -4
\]
\[
-13 + (x - 3)^2 = -4
\]

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

\[
(x - 3)^2 = -4 + 13
\]
\[
(x - 3)^2 = 9
\]

Now, we take the square root of both sides:

\[
x - 3 = \pm 3
\]

This gives us two equations to solve:

1. \(x - 3 = 3\)
2. \(x - 3 = -3\)

For the first equation:

\[
x = 3 + 3 = 6
\]

For the second equation:

\[
x = 3 - 3 = 0
\]

Thus, the solutions to the equation are:

\[
\{6, 0\}
\]

It seems that this solution set is not present in the original options provided. Let's double-check the calculations:

Starting from:

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

We simplified to:

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

And from that, the square root solutions were correct. My calculations and solutions are as follows:

- \(x = 6\)
- \(x = 0\)

Double-checking the final solutions, \{6, 0\} does not match any of the provided choices.

Please recheck the original equation for possible mistakes. If the equation is indeed correct, the solutions are \{6, 0\}, which isn't in the provided options.