To solve the quadratic equation \(x^2 - 6x - 16 = 0\) using the quadratic formula, we can use the formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
In this equation, \(a = 1\), \(b = -6\), and \(c = -16\).
Now, we can substitute 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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Substitute into the quadratic formula: \[ x = \frac{-(-6) \pm \sqrt{100}}{2(1)} = \frac{6 \pm 10}{2} \]
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This gives us two possible solutions:
- For the positive solution: \[ x = \frac{6 + 10}{2} = \frac{16}{2} = 8 \]
- For the negative solution: \[ x = \frac{6 - 10}{2} = \frac{-4}{2} = -2 \]
Thus, the solutions to the equation \(x^2 - 6x - 16 = 0\) are: \[ x = 8 \quad \text{and} \quad x = -2 \]
The correct response from your options would be: x=8, x=−2 (x equals 8, x equals negative 2).