Bot GPT 4-o mini To solve the quadratic equation \( x^2 - 6x - 16 = 0 \) using the quadratic formula, we use:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
In this case, the coefficients are:
- \( a = 1 \)
- \( b = -6 \)
- \( c = -16 \)
Now, we can plug these values into the formula:
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Calculate the discriminant (\( b^2 - 4ac \)): \[ b^2 - 4ac = (-6)^2 - 4(1)(-16) = 36 + 64 = 100 \]
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Now substitute back into the formula: \[ x = \frac{-(-6) \pm \sqrt{100}}{2(1)} = \frac{6 \pm 10}{2} \]
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This results in two potential solutions:
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For the plus sign: \[ x = \frac{6 + 10}{2} = \frac{16}{2} = 8 \]
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For the minus sign: \[ x = \frac{6 - 10}{2} = \frac{-4}{2} = -2 \]
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Thus, the solutions are \( x = 8 \) and \( x = -2 \).
The correct response is x=8, x=−2.
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