find all the real solutions. Are the real solutions the answers? 12x^2 + 2x -2 = 0

Question

find all the real solutions. Are the real solutions the answers?    12x^2 + 2x -2 = 0

anonymous · Answer

please wait...i will give you the answers...

lilsis76 · Answer

okay, thank you. I just dont know where or how to start the steps to solving. I have a very hard time with doing the first term higher than 2x^2. that is where i start panicking.

debbieg · Answer

You have a common factor of 2 that you can divide through by. Then it will factor. Once you have it factored, you just get one solution from each of the linear factors. :)

Don't panic, this is not that hard!

lilsis76 · Answer

haha I know its not hard, but the way I see it looks complicated. okay then I have this:
$$2(6x ^{2}+x-1)$$ @DebbieG

debbieg · Answer

$$\Large 12x^2 + 2x -2 =0$$$$\Large 6x^2 + x -2 =0$$

debbieg · Answer

Excellent! Now... it's an equation, so you can divide both sides by that 2, and you have what I show above. That's an EQUIVALENT EQUATION to what you started with, so has the same solutions, so now you just have to solve THAT.

Do you know how to solve it? HINT: If that left side FACTORS, that's usually the easiest way to go!

debbieg · Answer

oops, wait, my last term should be -1, lol

debbieg · Answer

you had it right though :)$$\Large 6x^2 + x -1 =0$$

anonymous · Answer

do you have the answer now?

anonymous · Answer

I found the answer!

lilsis76 · Answer

SORRY GUYS! I lost connection. Im back

debbieg · Answer

welcome back :)

lilsis76 · Answer

thank you Debbie :) okay so i had that answer you had 2(6x^2 +x -1) =0

lilsis76 · Answer

how can i factor the inside if there is a 6x^2?? I got...hold on let me see what I got

debbieg · Answer

Right, and then just divide through by that pesky 2, we don't need it. So the equation becomes:$$\Large 6x^2 + x -1 =0$$

lilsis76 · Answer

i got a -2 and +3 from factoring, is this correct?

debbieg · Answer

Do some trial and error. You need a product of 6(-1)=-6 that sumes to +1.

debbieg · Answer

*sum

anonymous · Answer

$$\Delta $$
@DebbieG  you want to continue with Delta?

debbieg · Answer

Show your factored form of the trinomial, what did you get?

(.........)(........)

lilsis76 · Answer

how did you get a +1? I dont think Delta, I dont know what that is

debbieg · Answer

I don't know what you mean either, @PFEH.1999 . Just need to factor that left hand side.

debbieg · Answer

Crud, sorry, I meant sums to -1.... LOL!

lilsis76 · Answer

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