To determine where Hyung-eun might have made an error in solving the quadratic equation \(x^2 - 4x - 12 = 0\), let's go through the typical steps of solving a quadratic equation by factoring or completing the square.
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Rearranging (if necessary): The equation is already in standard form.
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Factoring: We need to factor \(x^2 - 4x - 12\). We're looking for two numbers that multiply to \(-12\) (the constant term) and add up to \(-4\) (the coefficient of \(x\)): The numbers that satisfy this are \(-6\) and \(2\): \[ x^2 - 4x - 12 = (x - 6)(x + 2) = 0 \]
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Setting each factor to zero: \((x - 6) = 0\) or \((x + 2) = 0\) This leads to: \[ x = 6 \quad \text{or} \quad x = -2 \]
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Checking: You can verify by plugging \(x = 6\) and \(x = -2\) back into the original equation to ensure that both satisfy it.
Now, if Hyung-eun used a different method like grouping or incomplete factoring and made any algebraic mistakes along the way (such as a sign error, coefficient mistake, or miscalculation), we would need to see her specific work or steps to identify the error.
If you provide Hyung-eun's specific steps as she worked through the problem, I can help pinpoint where she first made an error.