## anonymous one year ago How do I do 7x^2 + x + 2 = 0 by the quadratic formula. Thanks for your help in advance!

1. DanJS

do you know the quadratic formula?

2. anonymous

I think so

3. DanJS

ax^2 + bx + c = 0 7x^2 + 1x + 2 = 0

4. DanJS

use those values for a, b , and c

5. anonymous

a = 7 b = 1 c = 2?

6. DanJS

yep.. $x=\frac{ -b \pm \sqrt{b^2-4ac} }{ 2a }$

7. anonymous

|dw:1441589861398:dw|

8. DanJS

the stuff under the square root turns out to be negative, so no real solutions to this one, less you want the complex roots

9. DanJS

$\sqrt{-1}=i$

10. anonymous

I do not know how to solve this from start to finish.

11. DanJS

you have it right so far with the drawing, just have to simplify it down now if needed.

12. anonymous

I tried it but when it got down to the imaginary number it got confusing.

13. DanJS

$x=\frac{ -1 \pm \sqrt{-55}}{ 14 }$ $x=\frac{ -1 }{ 14 }\pm \frac{ \sqrt{55} *\sqrt{-1}}{ 14 }$

14. anonymous

|dw:1441590203726:dw|

15. DanJS

just have to remember...$i=\sqrt{-1}$ put in i for that then solve normally

16. DanJS

$x =\frac{ -1 }{ 14 }+\frac{ \sqrt{55} }{ 14 }*i ~~~~~or~~~~~x =\frac{ -1 }{ 14 }-\frac{ \sqrt{55} }{ 14 }*i$

17. anonymous

Oh thank you I never knew what a imaginary number was.

18. anonymous

Does it simplified more is that the final answer?

19. DanJS

welcome, If you have to know nothing else about imaginary numbers, then just remember $i^2=-1~~~~or~~~~~i=\sqrt{-1}$

20. DanJS

that is all you can do to make it more simple looking

21. anonymous

Thanks so much! Did the i get in the problem because square root of 55 is a decimal?

22. DanJS

no, because the quadratic formula turned out to have a negative number in the square root, remember you cant take the square root of a number smaller than zero

23. DanJS

b^2 - 4*a*c was -55

24. anonymous

Oh okay I see how it got in then. Thanks for your time and help!