Question

How do you solve `y^2 - 3y - 14 = 0` by completing the square?

Answer 1

`(y-(3/2))^2 = y^2 - 3y + 9/4`,
so `y^2 - 3y - 14 = (y - 3/2)^2 - (14+9/4)`
`= (y-3/2)^2 - 65/4`.

And, since we are given that `y^2 - 3y - 14 =0`

`(y - 3/2)^2 = 65/4`

Hence `y = +-sqrt(65/4)+3/2 = +-sqrt(65)/2+3/2`.