To solve the quadratic equation \( x^2 - 6x - 16 = 0 \) using the quadratic formula, we use:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
For the equation \( ax^2 + bx + c = 0 \), the coefficients are as follows:
- \( a = 1 \)
- \( b = -6 \)
- \( c = -16 \)
Now, we can plug these values into the quadratic formula:
-
Calculate \( b^2 - 4ac \): \[ b^2 = (-6)^2 = 36 \] \[ 4ac = 4 \times 1 \times (-16) = -64 \] \[ b^2 - 4ac = 36 - (-64) = 36 + 64 = 100 \]
-
Now, substitute back into the formula: \[ x = \frac{-(-6) \pm \sqrt{100}}{2 \cdot 1} \] \[ x = \frac{6 \pm 10}{2} \]
-
Now we can split this into the two possible solutions: \[ x_1 = \frac{6 + 10}{2} = \frac{16}{2} = 8 \] \[ x_2 = \frac{6 - 10}{2} = \frac{-4}{2} = -2 \]
Thus, the solutions to the equation \( x^2 - 6x - 16 = 0 \) are \( x = 8 \) and \( x = -2 \).
Therefore, the correct response is: x=8, x=−2 x equals 8 , x equals negative 2
1 answer