Question

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.

Answer 1

need help bad

Answer 2

sqrt of the -700 is 26.4 and now im stuck

Answer 3

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

Answer 4

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

Answer 5

350?

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

350and 2?

Answer 10

that can get you 700?

Answer 11

identical question answered here
http://openstudy.com/study#/updates/55ff6651e4b0b395cadc64aa

Answer 12

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 ?

Answer 13

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

Answer 14

what factors do you mean? like single digit numbers?

Answer 15

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

Answer 16

wait here are what i know

Answer 17

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

Answer 18

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

Answer 19

what about 100 ?
we need GREATEST factor

Answer 20

oh

Answer 21

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

Answer 22

yeperz 10 x 10

Answer 23

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

Answer 24

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 \[\huge\rm \sqrt{-1} =i\]

Answer 25

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

Answer 26

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.

Answer 27

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

Answer 28

alright so whats next then?

Answer 29

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

Answer 30

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?

Answer 31

\[\huge\rm \frac{ -10 \pm \sqrt{\color{Red}{-1 \times 100 \times 7}} }{ 2 }\]
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

Answer 32

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

Answer 33

yep i have seen that before.

Answer 34

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

Answer 35

sqrt of 100 10x10?

Answer 36

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} =?

Answer 37

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

Answer 38

yes right !

Answer 39

and sqrt{-1} =what ?

Answer 40

{-1} {-1}?

Answer 41

you write it twice right ?

Answer 42

hmm reread my comments

Answer 43

your adding what the sqrt{-1}?

Answer 44

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

Answer 45

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

Answer 46

I as 1 or i lol ?

Answer 47

i

Answer 48

in latex I see -1 x 100 x 7?

Answer 49

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

Answer 50

http://prntscr.com/8iohs8

Answer 51

yeah i said it was i

Answer 52

remember what is common in both terms ?