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Students are presented with an AI generated solution to rerrange the quadratic equation where the AI has made errors, they are asked to identify on which line the first error occurs, then rewrite the solution correctly. No variables but this is 1 of 5 versions of the question.

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The error here occurs at line 7 when dividing by \\(-4a\\).

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The corrected solution starting at line 7 should be:

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  1. Divide both sides by \\(-4a\\) : \\(-ax^2 - bx = c\\)
    2. \n
  2. Now, \\(c\\) is the subject of the equation: \\(c = -ax^2 - bx\\)
    3. \n
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I asked an AI chat program to rearrange \\(\\displaystyle{x=\\frac{-b+\\sqrt{b^2-4ac}}{2a}}\\) to make \\(c\\) the subject. The response was:

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To rearrange the quadratic formula \\(\\displaystyle{x=\\frac{-b+\\sqrt{b^2-4ac}}{2a}}\\) to make \\(c\\) the subject, follow these steps:

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  1. Start with the equation:\\(\\displaystyle{x=\\frac{-b+\\sqrt{b^2-4ac}}{2a}}\\)
    2. \n
  2. Multiply both sides by \\(2a\\): \\(2ax = -b + \\sqrt{b^2 - 4ac}\\)
    3. \n
  3. Add \\(b\\) to both sides: \\(2ax + b = \\sqrt{b^2 - 4ac}\\)
    4. \n
  4. Square both sides: \\((2ax + b)^2 = b^2 - 4ac\\)
    5. \n
  5. Expand the left sides: \\(4a^2x^2 + 4abx + b^2 = b^2 - 4ac\\)
    6. \n
  6. Subtract \\(b^2\\) from both sides:\\(4a^2x^2 + 4abx = -4ac\\)
    7. \n
  7. Divide both sides by \\(-4a\\) : \\(-a^2x^2 - abx = c\\)
    8. \n
  8. Now, \\(c\\) is the subject of the equation: \\(c = -a^2x^2 - abx\\)
    9. \n
\n

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On which line does the first error occur? In your handwritten notes write out the solution to this problem correctly.

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