## some.random.cool.kid one year ago The complex solution to a quadratic equation is x equals start fraction negative 10 plus or minus square root of negative 700 end square root over two end fraction full stop Write this solution in standard form, x = a ± bi, where a and b are real numbers. Justify your answer by showing your work.

1. some.random.cool.kid

2. some.random.cool.kid

sqrt of the -700 is 26.4 and now im stuck

3. some.random.cool.kid

4. some.random.cool.kid

thats the image I just attached the file instead because the writing was to messy.

5. Nnesha

don't use calculator forsqrt{-700} there is a negative sign so you should get imaginary solution so factor out the -700 what is the largest factor of 700 that should be the perfect square root

6. some.random.cool.kid

350?

7. some.random.cool.kid

idk a perfect sqrt for 700 close ive got is 26.4 and thats a decimal

8. Nnesha

hmm 350 isn't a perfect square root what two numbers would you multiply to get 700 ??

9. Nnesha

here are some example of perfect square root sqrt{16}= 4 sqrt{25}=5

10. some.random.cool.kid

350and 2?

11. some.random.cool.kid

that can get you 700?

12. anonymous

13. Nnesha

like i said $\sqrt{350} = 18.7$ you will get decimal answer so 350 isn't a perfect square what are the factors of 700 ?

14. some.random.cool.kid

please walk me through this too i dont want a straight answer

15. some.random.cool.kid

what factors do you mean? like single digit numbers?

16. Nnesha

yes like factors of 9 are 1 and 3 ,9 in other words 9 is divisible by 1 and 3 and 9

17. some.random.cool.kid

wait here are what i know

18. some.random.cool.kid

1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70? do any those work?

19. some.random.cool.kid

if not im not sure what other factors their are for 700

20. Nnesha

what about 100 ? we need GREATEST factor

21. some.random.cool.kid

oh

22. Nnesha

7 times 100 = 700 and 100 is perfect square root ?

23. some.random.cool.kid

yeperz 10 x 10

24. some.random.cool.kid

so what do I do with this -700 then now that we figured out the two multiples?

25. Nnesha

yes right so we can writeh -700 as -1*7*100 100 bec we need greatest factor and sqrt{-1} bec we can change that to i $\huge\rm \sqrt{-1} =i$

26. Nnesha

$\huge\rm \frac{ -10 \pm \sqrt{-1 \times 100 \times 7} }{ 2 }$ sqrt{100} = 10 and replace sqrt{-1} with i

27. some.random.cool.kid

ah ha ok ok quick questions Im not sure if what I learned is the best method for a short cut but can I divide both the -10 and that sqrt by 2? and then I believe there is some final step afterwards.

28. Nnesha

first deal with the square root part then you can take out the common factor at the numerator after that you will be able to divide by 2

29. some.random.cool.kid

alright so whats next then?

30. Nnesha

alright so sqrt{-700}= what ??(not the decimal answer)

31. some.random.cool.kid

xD thats funny because I was about to put the decimal again thanks for clarifying lol. So based off of what I see you've got the 7 and 100 as your two multiples correct?

32. Nnesha

$\huge\rm \frac{ -10 \pm \sqrt{\color{Red}{-1 \times 100 \times 7}} }{ 2 }$ that's what we got whenever you see negative sign under the square root you should know that u have to take out the negative -1 so we can convert it to i

33. Nnesha

$\huge\rm \frac{ -10 \pm \sqrt{\color{Red}{-1 \times 100 \times 7}} }{ 2 }$ can be written as $\frac{ -10 \pm \sqrt{-1}\sqrt{100}\sqrt{7} }{ 2}$

34. some.random.cool.kid

yep i have seen that before.

35. Nnesha

now simplify sqrt{100} =? sqrt{-1}=?

36. some.random.cool.kid

sqrt of 100 10x10?

37. Nnesha

you can write 100 as 10 times 10 (and when we multiply same bases we should ADD their exponents ) so 10 times 10 = 10^2 sqrt{10^2} =?

38. some.random.cool.kid

wait isn't the sqrt of 10^2 the same as saying just 10?

39. Nnesha

yes right !

40. Nnesha

and sqrt{-1} =what ?

41. some.random.cool.kid

{-1} {-1}?

42. some.random.cool.kid

you write it twice right ?

43. Nnesha

44. some.random.cool.kid

45. some.random.cool.kid

sqrt -1 all i see that is would be { I }

46. Nnesha

i'm asking sqrt{-1} equal to what scroll up you will see huge latex!

47. Nnesha

I as 1 or i lol ?

48. some.random.cool.kid

i

49. some.random.cool.kid

in latex I see -1 x 100 x 7?

50. Nnesha

$\frac{ -10 \pm 10i \sqrt{7} }{ 2 }$ now you can take out the common factor at the numerator

51. Nnesha
52. some.random.cool.kid

yeah i said it was i

53. Nnesha

remember |dw:1442804236685:dw|what is common in both terms ?

54. some.random.cool.kid

sorry uh is that 10i?

55. Nnesha

|dw:1442804384787:dw| there is no eye(i) in first term

56. some.random.cool.kid

the only common I see is the 7 and -10 because they are like terms where as the 10i is not same

57. some.random.cool.kid

no in second term you drew in extra line so I couldnt tell I was asking if that was an i

58. Nnesha

let me explain |dw:1442804430474:dw| there are two box red and blue what is the common number in both terms ?

59. some.random.cool.kid

well there is two 10's?

60. Nnesha

yes right take it out

61. some.random.cool.kid

ok so ow your left with i x sqrt of 7?

62. some.random.cool.kid

now*

63. Nnesha

what will you get when you take out 10 from -10?

64. Nnesha

or in other words divide 10 by common factor so -10/10 = ?

65. some.random.cool.kid

or is it i = sqrt of 7 and doesn't that cancel out?

66. some.random.cool.kid

that should cancel out because one is negative and both same numbers

67. Nnesha

no 2/2 would be 1 so 10/10 ?

68. some.random.cool.kid

wait 1?

69. Nnesha

yes right $\frac{ 10(-1 \pm i \sqrt{7} )}{ 2 }$

70. Nnesha

NOW you can divide 10 by 2

71. Nnesha

got one mint :D

72. some.random.cool.kid

so thats 5 uh one minute? you mean or like candy mint

73. Nnesha

$5(-1 \pm i \sqrt{7})$ now you can distribute by 5

74. Nnesha

no i have to go

75. some.random.cool.kid

because i needed help with one more but if you have to go i can respect that

76. some.random.cool.kid

ok bye

77. Nnesha

alright hope that hlped sorry but gtg