Question

using the quadratic formula, fine the solution to x^2 - 6x - 16 = 0

Answer 1

To find the solutions to the quadratic equation x^2 - 6x - 16 = 0 using the quadratic formula, we will use the formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Here, a = 1, b = -6, and c = -16.

Plugging these values into the formula, we get:

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

So, the two solutions to the equation x^2 - 6x - 16 = 0 are:

x₁ = (6 + 10) / 2 = 16 / 2 = 8
x₂ = (6 - 10) / 2 = -4 / 2 = -2

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