To solve the quadratic equation \(x^2 - 6x - 16 = 0\) using the quadratic formula, we can follow these steps:
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Identify the coefficients for the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\).
- Here, \(a = 1\), \(b = -6\), and \(c = -16\).
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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 the values into the quadratic formula: \[ x = \frac{-(-6) \pm \sqrt{100}}{2(1)} = \frac{6 \pm 10}{2}. \]
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Calculate the two possible values for \(x\): \[ x = \frac{6 + 10}{2} = \frac{16}{2} = 8, \] \[ x = \frac{6 - 10}{2} = \frac{-4}{2} = -2. \]
Thus, the solutions are \(x = 8\) and \(x = -2\).
The final answer is: x = 8, x = -2 (or x equals 8, x equals negative 2).