## anonymous 3 years ago Can someone explain to me, STEP BY STEP how to do this problem please, its Algebra 2-Complex numbers. -6(x+5)^2=120

1. hartnn

first divide both sides by -6 what u get ?

2. hartnn

and u should know that $$\huge \sqrt{-1}=i$$

3. anonymous

6(x+5)^2+120 = (x+5)^2 - 20i^2 =0 ( and then factorise ) as i^2 =-1

4. anonymous

hartn good explanation and asking for participation . well done !!

5. anonymous

|dw:1352352097064:dw|

6. richyw

$-6(x+5)^2=120$$(x+5)^2=-\frac{120}{6}$$x+5=\sqrt{-\frac{120}{6}}$$x+5=\sqrt{-20}$$x=\sqrt{-20}-5$$x=\sqrt{20}i-5$$x=\sqrt{4\cdot 5}i-5$x=2\sqrt{5}i-5

7. anonymous

Now take the square root of the RHS .

8. richyw

$x=2\sqrt{5}i-5$

9. anonymous

10. hartnn

i don't think @CarolineJean wants any of your solutions, she wants to understand and none of you are helping by giving steps out...

11. anonymous

@hartnn yeah, thanks :)

12. richyw

oops just forgot the $$\pm$$

13. anonymous

Now take the square root. What do you get?

14. anonymous

I don't think you HAVE to simplify...

15. richyw

I dunno it's how I learn. sorry. I will leave.

16. anonymous

wow thanks everyone that helped alot :O i have a test tomorrow & didn't know how to do this type of problem but i understand now, thanks ^.^

17. anonymous

you go hartn !

18. anonymous

Ohh you understand? :) Good :) .

19. anonymous

omg the whole time i was trying to figure out how to do it i was trying to figure out how everyone was getting 20... i feel dumb now.... x)

20. anonymous

Haha :) .

21. richyw

if you are following my (huge list) of steps. just don't forget to take bot the positive and negative root. So you should get $$x=-2i\sqrt{5}-5$$ and $$x=2i\sqrt{5}-5$$

22. hartnn

x=.... OR x=... either of them is a solution, not both

23. anonymous

yay ! i got that ! @richyw

24. anonymous

thank you to the only 2 ppl that really explained what to do lol @hartnn @richyw

25. anonymous

Not me? ;) . Jk Jk . Glad you understood :) .

26. anonymous

sorry didn't see yours ! :O @Dido525