Question

How do you solve the quadratic equation by completing the square: `y^2+3y=10`?

Answer 1

`y=2 or y=-5`

Explanation:

`y^2 +3y" "= 10`

You want to add in a missing term on the left so that you have a perfect square trinomial which can then be written in the form
`(y +?)^2` This process is called 'completing the square.'

The 'missing term' is found from `(b/2)^2` and has to be added to both sides of the equation.

`y^2 +3y" "color(blue)( +(3/2)^2) = 10" " color(blue)(+(3/2)^2)`

The left side can now be written as `(y+?)^2` and the right side can be simplified.

`(y +3/2)^2 = 10 +9/4" "larr` square root both sides

`(y+3/2) = +-sqrt(10 +2 1/4) = +-sqrt(12 1/4)`

`y +3/2 = +-sqrt(49/4)`

`y = 7/2-3/2" "or" "y = -7/2-3/2`

`y = 4/2=2" "or " "y= -10/2=-5`