To solve the quadratic equation \(x^2 - 6x - 16 = 0\) using the quadratic formula, we use the formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
For the given equation, the coefficients are:
- \(a = 1\)
- \(b = -6\)
- \(c = -16\)
Now, we can plug these values into the formula.
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First, calculate the discriminant (\(b^2 - 4ac\)): \[ b^2 = (-6)^2 = 36 \] \[ 4ac = 4 \cdot 1 \cdot (-16) = -64 \] \[ b^2 - 4ac = 36 - (-64) = 36 + 64 = 100 \]
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Now we can find \(x\) using the quadratic formula: \[ x = \frac{-(-6) \pm \sqrt{100}}{2 \cdot 1} \] \[ x = \frac{6 \pm 10}{2} \]
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This gives us two possible solutions: \[ x = \frac{6 + 10}{2} = \frac{16}{2} = 8 \] \[ x = \frac{6 - 10}{2} = \frac{-4}{2} = -2 \]
The solutions to the equation \(x^2 - 6x - 16 = 0\) are: \[ x = 8 \quad \text{and} \quad x = -2 \]
Thus, the correct response is: x=8, x=−2 or x equals 8, x equals negative 2.
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