Question

How do you solve by completing the square: `x^2+5/2x=5`?

Answer 1

To complete the square on the left side we need to add the square of half of the coefficient of the `x` term.
(This follows from the observation `(x+a)^2 = x^2+2ax+a^2`)

`x^2+5/2x+ (5/4)^2 = 5 + (5/4)^2`

`(x+5/4)^2 = 105/16`

Taking the square root of both sides
`x+5/4 = +-sqrt(105)/4`

So
`x= -(5+sqrt(105))/4`
or
`x = -(5-sqrt(105))/4`