9y^2+2=9y

Question

9y^2+2=9y

tkhunny · Answer

Have you considered putting it in standard form so it looks like a Quadratic Equation - the sort of thing you have solved already, many times?

anonymous · Answer

idk how to do that.

phi · Answer

add -9y to both sides

anonymous · Answer

thats how it was wrote

tkhunny · Answer

You don't know how to put it in standard form?  Can you do as phi suggested?

anonymous · Answer

yes

tkhunny · Answer

Okay, show the standard form.

anonymous · Answer

-9y+9y^2+2=0?

phi · Answer

yes, but you should write it in descending exponents.  (the -9y   is the same as -9y^1
and it comes after the 9y^2

tkhunny · Answer

Descending exponents.  Try to make the first coefficient positive.

anonymous · Answer

so 9y^2-9y+2=0

phi · Answer

yes.  
this one can be factored, but it's tricky

anonymous · Answer

how do you do that?

phi · Answer

if we multiply the 9 from y^2  times the (last) 2 we get 18

we now list all ways of multiplying 2 numbers to get 18:
1,18
2,9
3,6

phi · Answer

the + on the +2 means the roots are the same sign
the - on the -9y means the "bigger" root is negative.

together , both of these rules means both roots are negative.

we look at our list of pairs, making both numbers negative, and add them up
-1-18= -19
-2-9 = -11
-3 - 6 = -9

look for the pair that give a -9  (to match the -9y term)

phi · Answer

we see -3 and -6 are the pair.

the 2 must divide into one of these numbers (the -6) to get
-3, -2, 3

this means (how to explain!?)
(3y -1)(3y-2)=0

anonymous · Answer

is that the answer? cause this is still so confusing.

phi · Answer

you have two terms that could be 0  (and make the equation true)
can you solve them?
3y-1=0
and
3y-2= 0

anonymous · Answer

-3 and -1.5

tkhunny · Answer

Try that first one again.

anonymous · Answer

3

tkhunny · Answer

3y - 1 = 0

add 1

3y = 1

Divide by 3

y = 1/3

You seem to be guessing.

anonymous · Answer

i was dividing it by 1. im not thinking im sorry

tkhunny · Answer

It's okay.  Take a deep breath.  :-)

Now check.

9y^2+2=9y

Substitute those values and make sure they work.

anonymous · Answer

9(1/3)^2+2=9(1/3)
1+2=3
3=3

tkhunny · Answer

One down.  How about the other one?

anonymous · Answer

what am i plugging in?

tkhunny · Answer

You are not "plugging in" anything.

Substitute the value y = -1.5, the other one you determined by factoring.

anonymous · Answer

9(-1.5)^2+2=9(-1.5)
is that how i set it up?

tkhunny · Answer

That's it.  Why would it be different from y = 1/3?  Substitute and go!