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

Question

.(1 point)
Responses

{16,−10}
left brace 16 comma negative 10 right brace

{8,−2}
left brace 8 comma negative 2 right brace

{2,−8}
left brace 2 comma negative 8 right brace

{28,−22}

Answer 1

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

1. Clear the equation of constants: \[ -9 + (x - 3)^2 - 4 = -4 \] simplifies to: \[ (x - 3)^2 - 13 = -4 \] Adding 13 to both sides: \[ (x - 3)^2 = 9 \]

2. Next, take the square root of both sides: \[ x - 3 = \pm 3 \]

3. Now, solve for \( x \):

   • For the positive case: \[ x - 3 = 3 \implies x = 6 \]
   • For the negative case: \[ x - 3 = -3 \implies x = 0 \]

Putting both solutions together, we have: \[ {6, 0} \]

However, this doesn't match any of your given options. It seems there may be a misunderstanding or error in transcribing the equation or options. Please double-check the equation or the potential answers provided.

If we revisit the simplification and computation steps, we can confirm that the solutions from the given equation should indeed yield \( x = 6 \) and \( x = 0 \). If the question or options are different, let me know for further clarification.