anonymous 5 years ago i have the answer but the problem but no explanation.. i need to know how to solve this. how do i get there. thanks. 4x2 = -8x -1 the answer comes out to this fraction -2 ±√3 ________ 2

1. anonymous

and the problem... here is a picture just in case

2. anonymous

use the quadratic formula after getting all terms on one side 4x2+8x+1 so a=4, b=8, and c=1 plug into qf

3. anonymous

did you take a look at the picture? it didnt type out correctly. sorry. i really appreciate your help.

4. anonymous

I understood the problem..do you know the quadratic formula?

5. anonymous

not really

6. anonymous

ok I will type it out

7. anonymous

thank you so much

8. anonymous

$-b \pm \sqrt{b ^{2}-4ac}/2a$

9. anonymous

2a is in the denominator so substitute a, b, and c

10. anonymous

$-8 \pm \sqrt{64-16}/ 8$

11. anonymous

$-8\pm \sqrt{48}/8 = -8\pm \sqrt{16*3} /8 -8\pm4\sqrt{3} /8$

12. anonymous

I skipped the initial step of plugging in the values for a, b, and c do you get that part?

13. anonymous

yes i do thank you

14. anonymous

so do you understand it

15. anonymous

its for friend, but yes i think so. im passing the info along. thank you for your time.

16. anonymous

ok you're very welcome

17. anonymous

one last question.. how did you know that the qf was necessary? just in case other problems like these come up. how can i decipher whether i need it or not.

18. anonymous

if you can't solve the quadratic equation by factoring then your other options are by completing the square or the quadratic formula

19. anonymous

not sure if youre still there, but one thing my friend didnt understand was how it was simplified to the final answer. isnt the 4 outside the square root technically tied to it and you can't really simplify it?

The simplification was valid. The 48 inside the radical was factored to 16 and 3, the square root of 16 was accomplished by moving the 4 outside of the radical leaving only the square root of 3 within the radical.

The simplification of$-8\pm(4\sqrt{3})/8=-4(2\pm \sqrt{3})/8=(-2\pm \sqrt{3})/2$