133k views
0 votes
Solve 2y²+9y+10=0 by completeing square method?

User Aashii
by
8.0k points

1 Answer

4 votes

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 :)

User Ambulare
by
7.9k points