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

x=−2
x equals negative 2

x=8, x=−2
x equals 8 ,  x equals negative 2

x=8

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 this equation, $ a = 1 $, $ b = -6 $, and $ c = -16 $. 1. Calculate the discriminant ($ b^2 - 4ac $): $$ b^2 = (-6)^2 = 36 $$ $$ 4ac = 4 \times 1 \times (-16) = -64 $$ $$ b^2 - 4ac = 36 - (-64) = 36 + 64 = 100 $$ 2. Now apply the quadratic formula: $$ x = \frac{-(-6) \pm \sqrt{100}}{2 \times 1} = \frac{6 \pm 10}{2} $$ 3. Find the two potential solutions: $$ x_1 = \frac{6 + 10}{2} = \frac{16}{2} = 8 $$ $$ x_2 = \frac{6 - 10}{2} = \frac{-4}{2} = -2 $$ Thus, the solutions are: $$ x = 8, \quad x = -2 $$ The correct response is: **x=8, x=−2**.