How do you solve w^2/24-w/2+13/6=0 by completing the square?

1 Answer
Jul 18, 2016

The solutions will be w = 6 +- 4i.

Explanation:

We can start by removing fractions from the mix by multiplying both sides by 24:
w^2 - 12w + 52 = 0

Now observing that we need an equation looking like w + b where 2b = -12 it is clear that the squared term will be w - 6.

Since (w-6)^2 = w^2 - 12w + 36 we can take 36 out of 52, this gives us:
(w-6)^2 + 16 = 0

we can manipulate this:
(w-6)^2 = -16

And take the square root of both sides:
w-6 = +- 4i
w = 6 +- 4i

You can check this answer by inputting the coefficients into the quadratic equation as well.