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

Question

Responses

{28,−22}
left brace 28 comma negative 22 right brace

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

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

{8,−2}

Answer 1

To solve the quadratic equation \( -9 + (x - 3)^2 - 4 = -4 \) using square roots, we will first simplify the equation.

1. Start by simplifying the left side: \[ -9 + (x - 3)^2 - 4 = -4 \] Combine like terms: \[ (x - 3)^2 - 13 = -4 \] Add 13 to both sides: \[ (x - 3)^2 = 9 \]

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

3. Solve for \( x \):

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

4. The solutions to the equation are \( x = 6 \) and \( x = 0 \).

The solution set is \({6, 0}\), which does not match any of the given response options exactly. Please check the choices provided or reconsider the question's context. If you meant to set up a different equation or you have a choice that reflects the values of \(x\) as needed, ensure the equation correlates correctly for future resolutions.