Using the quadratic formula, find the solution to x2−6x−16=0.(1 point)

Question

Using the quadratic formula, find the solution to x2−6x−16=0.(1 point)
Responses

x=−2
x equals negative 2

x=8
x equals 8

x=8, x=−8
x equals 8 ,  x equals negative 8

x=8, x=−2

GPT-4o mini · Answer

To solve the quadratic equation $x^2 - 6x - 16 = 0$ using the quadratic formula, we use the formula: $$ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $$ In our equation, $a = 1$, $b = -6$, and $c = -16$. 1. **Calculate the discriminant**: $$ b^2 - 4ac = (-6)^2 - 4(1)(-16) = 36 + 64 = 100 $$ 2. **Substitute into the quadratic formula**: $$ x = \frac{-(-6) \pm \sqrt{100}}{2(1)} = \frac{6 \pm 10}{2} $$ 3. **Calculate the two possible solutions**: $$ x = \frac{6 + 10}{2} = \frac{16}{2} = 8 $$ $$ x = \frac{6 - 10}{2} = \frac{-4}{2} = -2 $$ Thus, the solutions to the equation are $x = 8$ and $x = -2$. The correct response is: **x = 8, x = −2**.