Answer:
y = -2 and -5/2
Explanation:
To complete the square, let's take 10 to the other side.
2y^2 + 9y = -10
Now let's divide by 2 on both sides
y^2 + 9/2y = -5
Now, let's complete the square by halving the b coefficient (9/2) and then squaring it.
9/2 * 1/2 = 9/4
(9/4)^2 = 81/16
Let's add 81/16 to both sides
y^2 + 9/2y + 81/16 = -5 + 81/16
Let's factor and simplify this now
(y + 9/4)^2 = 1/16
From here, we can square root both sides
y + 9/4 = 1/4
y + 9/4 = -1/4
Let's bring 9/4 over to the other side in both expressions and solve for the 2 possible y values. (we have to consider both the negative and positive values when we perform our own square root)
y = 1/4-9/4 = -8/4 = -2
y = -1/4 - 9/4 = -10/4 = -5/2
So our answer is y = -2 and -5/2
Hope this helps :)