How do you do this?

Question

solve the following equation by using the quadratic formula:

w^2-8w+19=0

Answer 1

The quadratic formula is

w = [-b +/- sqrt (b^2 - 4ac)] / 2a

In your equation, a = 1, b = -8, and c = 19. Plug and play!

w = [-b +/- sqrt (b^2 - 4ac)] / 2a
w = [-(-8) +/- sqrt ((-8)^2 - 4(1)(19))] / 2(1)
w = [8 +/- sqrt (64 - 76)] / 2
w = [8 +/- sqrt (-12)] / 2
w = [8 +/- i*sqrt (12)] / 2
w = [8 +/- 2i*sqrt (3)] / 2
w = 4 +/- i*sqrt (3)

Now if you're not into imaginary numbers, you can stop at the point where you realize that you have a negative square root issue and say that this equation has no real roots. But if you're into imaginary numbers, then the answer above is what you're looking for.