## anonymous one year ago FACTOR 2x^2 + x - 28 = 0 There should be 2 x's. I am stuck at 2(x^2+x-14)=0

1. anonymous

@haleyelizabeth2017 Lists steps

2. haleyelizabeth2017

Wait, it was originally $$2x^2+2x-28?$$

3. haleyelizabeth2017

What you have is the simplest it can go.

4. anonymous

Originally 2x^2+x-28=0

5. haleyelizabeth2017

Okay, then what you have so far is not correct.

6. anonymous

oh yea i made a mistake, i thought the GCF was 2 when it can't be

7. anonymous

what can be mult. to make -56 but added to make 1

8. haleyelizabeth2017

-7 and 4 multiply to get -28, okay? So then...if one side is (2x+/-_)(x+/-_) we can plug in those two numbers to try and see which works.

9. anonymous

im guessing that another way to do it Eli?

10. haleyelizabeth2017

So...let's try (2x-7)(x+4) first. We get $$2x^2+8x-7x-28$$ which simplified, would work. So, (2x-7)(x+4) is the correct.

11. haleyelizabeth2017

12. anonymous

so 2x-7=0 is x=7/2 or 3 1/2

13. anonymous

and x=-4

14. haleyelizabeth2017

Normally, it is left as an improper fraction, so x=7/2 is better. and x=-4 is correct as well.

15. haleyelizabeth2017

You could have also used the quadratic formula.

16. haleyelizabeth2017

It is a lot easier. Or, even complete the square works too

17. haleyelizabeth2017

$\frac{ -b \pm \sqrt{b^2-4ac} }{ 2a }$ $ax^2+bx+c=0$

18. anonymous

Ok, i got a question... the formula is ax^2+bx+c... i was told that you mult. a*c and the number that you get has to be mult. by x number and x number, but those two number must also be able to be added together to equal B... did that make sense

19. anonymous

Is there an exception to this??

20. haleyelizabeth2017

Huh?

21. haleyelizabeth2017

You don't have to do anything to the a b or c. just plug the coefficients into the quadratic formula and solve. Lets use your problem for example. We were given $2x^2+x-28$ A would be 2, b would be 1, and c would be -28.

22. haleyelizabeth2017

$\frac{ -(1) \pm \sqrt{(1)^2-4(2)(-28)} }{ 2(2) }$$\frac{ -1 \pm \sqrt{1+224} }{ 4 }$and so on

23. haleyelizabeth2017

Did that make sense?

24. Hero

@Beleaguer did you figure out What the two numbers are?

25. Hero

In other words, can you solve m+n =1 mn =-56