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

Question

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 equation \(-9 + (x - 3)^2 - 4 = -4\), first simplify the left side:

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

This simplifies to:

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

Now, add \(13\) to both sides:

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

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

Next, take the square root of both sides:

\[ x - 3 = \pm 3 \]

Now, solve for \(x\):

1. For the positive case: \[ x - 3 = 3 \implies x = 3 + 3 = 6 \]

2. For the negative case: \[ x - 3 = -3 \implies x = 3 - 3 = 0 \]

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

However, these values do not match any of the response sets provided, which suggests a reconsideration of the equation’s potential transformations or an error in the available options.

Double-checking our simplifications and isolations, there appears to be no deviation from the standard process:

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

\[ x = 0, 6. \]

Thus, the correct solutions are \( {0, 6} \), which may not align with the provided options, leading to a conclusion that none of the answers given in the options are correct.