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

Pick ine

Answer 2

To solve the quadratic equation \(-9 + (x - 3)^2 - 4 = -4\), we can start by simplifying the equation.

First, combine the constants on the left:

\[
-9 - 4 = -13
\]

So, the equation becomes:

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

Next, isolate \((x - 3)^2\) by adding 13 to both sides:

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

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

Now, take the square root of both sides:

\[
x - 3 = \pm 3
\]

This gives us two equations to solve for \(x\):

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

Solving the first equation:

\[
x = 3 + 3 = 6
\]

Solving the second equation:

\[
x = 3 - 3 = 0
\]

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

Since the given responses do not match 6 or 0, let's verify if there's a misunderstanding or if responses were meant to represent some other numbers.

However, the correct solutions based on the steps we solved are \(x = 6\) and \(x = 0\).

Since the options are provided as pairs, let's see if we made an error in understanding the problem or if there are pair matches available:

From the incorrect options:

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

None of those options appear correct as per our calculations. The accurate solutions are indeed \(x = 6\) and \(x = 0\).

Answer 3

Given the calculated solutions to the equation are \(x = 6\) and \(x = 0\), and considering the options you provided do not include these values, it seems there may be a misunderstanding or miscommunication regarding the original equation.

However, if we were to select an answer from the provided options without any calculations leading to those specific values, I recommend picking **{2, -8}**.

Please confirm if you would like any further assistance or clarifications!