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

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}

7 answers

To solve the quadratic equation \(-9 + (x - 3)^2 - 4 = -4\), we first simplify the equation:

  1. Move \(-4\) to the other side of the equation: \[ -9 + (x - 3)^2 = 0 \]

  2. Add \(9\) to both sides: \[ (x - 3)^2 = 9 \]

  3. Next, take the square root of both sides: \[ x - 3 = 3 \quad \text{or} \quad x - 3 = -3 \]

  4. Solve for \(x\) in both cases:

    • For \(x - 3 = 3\): \[ x = 6 \]
    • For \(x - 3 = -3\): \[ x = 0 \]

Thus, the solutions to the equation are \(x = 6\) and \(x = 0\). Therefore, the solution set is: \[ {6, 0} \]

Looking at the responses you've provided, none of the choices match the correct answer. If you were looking for a formatted response based on your options, the answer lies outside that choice set. The solutions \(x = 6\) and \(x = 0\) should be noted as the correct outcomes.

you have to choose one

Apologies for the confusion. Since I found the solutions \(x = 6\) and \(x = 0\), but those options are not available in your provided responses, it seems there might be a misunderstanding or error in the formulation of the options.

However, since the problem is to select one of the listed responses, and none are correct based on the solutions we derived, I suggest reconsidering if there might be a mistake in the options provided.

For the sake of choosing from your response set, I cannot accurately select one as being correct. It would be best to double-check the equation or the options given. If you still want me to pick one despite the misalignment, I'd go for the closest form, but do keep in mind that it's indeed incorrect.

If pressed to choose blindly among the options provided, I would select: \[ {2, -8} \] However, please check for clarity or updated choices or context regarding the problem itself. The actual correct results do not align with any of the options given.

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

Let's solve the equation step by step:

The equation provided is:

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

  1. Combine like terms on the left side: \[ -9 - 4 + (x - 3)^2 = -4 \] \[ -13 + (x - 3)^2 = -4 \]

  2. Isolate the square term: \[ (x - 3)^2 = -4 + 13 \] \[ (x - 3)^2 = 9 \]

  3. Take the square root of both sides: \[ x - 3 = 3 \quad \text{or} \quad x - 3 = -3 \]

  4. Solve for \(x\):

    • First equation: \[ x = 3 + 3 = 6 \]
    • Second equation: \[ x = 3 - 3 = 0 \]

So, we have the solutions \(x = 6\) and \(x = 0\).

Now, let's examine the provided responses:

  • \({28, -22}\)
  • \({2, -8}\)
  • \({16, -10}\)
  • \({8, -2}\)

None of these options include \(0\) or \(6\) as possible answers.

If we need to select an answer from the choices, we cannot accurately do so based on the calculation. Please double-check the equation or options given, as there might be an error in the problem setup.

If you need me to choose one from the options given without a correct basis, please clarify that, and I’ll choose the one you wish, but again, those do not relate to the actual solutions derived from the problem.

YOU HAVE TO CHOOSE ONE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

I apologize for the confusion in my previous responses. Given the urgency, I will select one of the provided options at random, since none are correct based on the equation solved.

I will choose: \({8, -2}\)

Please remember this choice does not reflect the actual solutions to the equation, as those are \(0\) and \(6\). Thank you for your patience!