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.

- some.random.cool.kid

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- some.random.cool.kid

need help bad

- some.random.cool.kid

sqrt of the -700 is 26.4 and now im stuck

- some.random.cool.kid

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- some.random.cool.kid

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

- 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

- some.random.cool.kid

350?

- some.random.cool.kid

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

- Nnesha

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

- Nnesha

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

- some.random.cool.kid

350and 2?

- some.random.cool.kid

that can get you 700?

- anonymous

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

- 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 ?

- some.random.cool.kid

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

- some.random.cool.kid

what factors do you mean? like single digit numbers?

- Nnesha

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

- some.random.cool.kid

wait here are what i know

- some.random.cool.kid

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

- some.random.cool.kid

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

- Nnesha

what about 100 ?
we need GREATEST factor

- some.random.cool.kid

oh

- Nnesha

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

- some.random.cool.kid

yeperz 10 x 10

- some.random.cool.kid

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

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

- Nnesha

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

- 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.

- 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

- some.random.cool.kid

alright so whats next then?

- Nnesha

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

- 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?

- 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

- Nnesha

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

- some.random.cool.kid

yep i have seen that before.

- Nnesha

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

- some.random.cool.kid

sqrt of 100 10x10?

- 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} =?

- some.random.cool.kid

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

- Nnesha

yes right !

- Nnesha

and sqrt{-1} =what ?

- some.random.cool.kid

{-1} {-1}?

- some.random.cool.kid

you write it twice right ?

- Nnesha

hmm reread my comments

- some.random.cool.kid

your adding what the sqrt{-1}?

- some.random.cool.kid

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

- Nnesha

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

- Nnesha

I as 1 or i lol ?

- some.random.cool.kid

i

- some.random.cool.kid

in latex I see -1 x 100 x 7?

- Nnesha

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

- Nnesha

http://prntscr.com/8iohs8

- some.random.cool.kid

yeah i said it was i

- Nnesha

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

- some.random.cool.kid

sorry uh is that 10i?

- Nnesha

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

- 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

- 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

- Nnesha

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

- some.random.cool.kid

well there is two 10's?

- Nnesha

yes right take it out

- some.random.cool.kid

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

- some.random.cool.kid

now*

- Nnesha

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

- Nnesha

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

- some.random.cool.kid

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

- some.random.cool.kid

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

- Nnesha

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

- some.random.cool.kid

wait 1?

- Nnesha

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

- Nnesha

NOW you can divide 10 by 2

- Nnesha

got one mint :D

- some.random.cool.kid

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

- Nnesha

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

- Nnesha

no i have to go

- some.random.cool.kid

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

- some.random.cool.kid

ok bye

- Nnesha

alright hope that hlped
sorry but gtg

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