Question

Using the quadratic formula, find the solution to x^2 – 6x – 16 = 0

Answer 1

To find the solution to the quadratic equation x^2 – 6x – 16 = 0, we will make use of the quadratic formula:

x = (-b ± √(b^2 - 4ac))/(2a)

In the given equation, a = 1, b = -6, and c = -16.

Plugging these values into the quadratic formula, we have:

x = (-(-6) ± √((-6)^2 - 4(1)(-16)))/(2(1))
= (6 ± √(36 + 64))/2
= (6 ± √100)/2
= (6 ± 10)/2

Now we have two possible solutions:

1. When x = (6 + 10)/2 = 16/2 = 8
2. When x = (6 - 10)/2 = -4/2 = -2

Hence, the solutions to the equation x^2 – 6x – 16 = 0 are x = 8 and x = -2.