Question

How do you solve using the completing the square method `0=x^2-3x-6`?

Answer 1

`x = 3/2 +- (33)^(1/2) / 2`

Explanation:

We need to add a number to create the constant
`(b/2)^2` which will make the perfect square `( x - (b/2))^2`
Since b = - 3 then `(b/2)^2 = 9/4`
But we already have - 6 = - 24/4 so we need to add 33/4
And we also need to subtract 33/4 to keep the equation true
This results in
`( x - (3/2))^2 = 33/4`
Taking the root and adding 3/2 to both sides
gives the result
`x = 3/2 +- (33)^(1/2) / 2`