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

Question

.(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.

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