Question

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

Answer 1

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.