Can someone explain one part of this question for me? (b) 3x^2 + 3x + 2y = 0?

Question

it asks me to

complete the square and

reduce to one of the standard forms

y − b = A(x − a)^2 or x − a = A(y − b)^2

now someone explained this already.. kind of but i really don't understand one of the steps and it wasn't clarified

Now, you want it to look like:

y − b = A(x − a)^2

So move the -1 to the other side. in this equation, A = 1, so don't worry about A.

y + 1= (x + 2)^2

and there you go! now, try to do b.

HINT: it's 3x^2 + 3x, so take out a 3 and complete the square

3x^2 + 3x + 2y = 0

3x^2 + 3x = - 2y

3(x^2 + x) = - 2y

Now complete the square in the brackets. you should get:

-3/2(x + .5)^2 = y - 3/8

WHY is there a - 3/8 besides the y? i don't understand where that - 3/8 came from, please help D:

Answer 1

-3/2(x + .5)^2 = y - 3/8

LHS : -3/2(x + .5)^2                           RHS: y - 3/8

if you were to expand -3/2( x + .5) ^2,you'll get

-3/2x^2  -3/2x - 3/8

bearing in mind the fact that

3x^2 + 3x + 2y = 0

LHS=RHS

therefore at RHS, put a -3/8  (hence RHS is y-3/8

Answer 2

When you get to 3(x^2 + x) = -2y you need to complete the square like this:

3(x^2 + 1x +__) = -2y + __

Divide 1 by 2 so it equals 1/2 or .5 which ever you prefer and then square it so it's 1/4. 1/4 would go into the blanks but because there is a 3 that has to be distributed then you have to multiple 3 x 1/4 to get what belongs in the blanks.

3 x 1/4 = 3/4

So now your problem looks like this:

3(x^2 + x + 3/4) = -2y + 3/4

Then you would simplify the stuff in the parentheses

3(x + .5)^2 = -2y + 3/4

Then divide all of it by -2

So then you would get

-3/2(x + .5)^2 = y - 3/8

You get the -3/8 because you had to divide the 3/4 by -2

Which is the same as multiplying 3/4 x -1/2 which = -3/8

Hope I helped!!

Answer 3

3(x^2 + x) = - 2y  until here it is clear, isn't it?

Now you should complete the full square in the brackets

(x^2+2*x*m+m^2 - m^2)  

- m^2 appears not to spoil !

You see that m=1/2  (2xm=x)    

and m^2=1/4 (you should add and subtract it!)

In the brackets    (x^2 + 2x*1/2 + 1/4 -1/4) = (x +1/2)^2 - 1/4

Turn to start

3(x+1/2)^2- 3/4 = - 2y  ( divide by 3)

(x+1/2)^2= - (2y)/3 + 1/4 this is the answer