Solve the quadratic equation x2 − 6x + 13 = 0 using the quadratic formula. What is the solution when expressed in the form a ± bi, where a and b are real numbers?
x = 3 ± 2i
x = 2 ± 3i
x = 3 ± 4i
x equals start fraction three plus or minus two i over two end fraction

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- some.random.cool.kid

please walk me thorugh...

- some.random.cool.kid

through* to get the right answr. @Nnesha

- some.random.cool.kid

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## More answers

- some.random.cool.kid

- DanJS

you know the quadratic formula that results from solving that standrard quadratic form for x =

- some.random.cool.kid

i knew it but forgot mind showing me it?

- DanJS

If ax^2 + bx + c = 0
\[x = \frac{ -b \pm \sqrt{b^2-4ac} }{ 2a}\]

- some.random.cool.kid

yes yess ik that ah thank ok so b is b 13 is c and 1 is a correct?

- some.random.cool.kid

thank you*

- some.random.cool.kid

oops i said b is bxD

- some.random.cool.kid

i meant b is 6

- DanJS

a = 1
b = -6
c = 13

- some.random.cool.kid

oops -6 not 6 ok

- DanJS

x^2 + (-6)x .....

- some.random.cool.kid

uh solve that?

- some.random.cool.kid

want me to solve it?

- DanJS

yeah , use those values and simplify as much as you can

- some.random.cool.kid

uh...wait step by step please what will this look like when finished finding each letter ot the number? can you rewrite for me but this time instead of variables substitute it with numbers so that i may have an idea in my mind i do better solving when i have a visual.

- DanJS

ill type it out fast, i have to run for a while ... one sec

- some.random.cool.kid

ok thank you

- DanJS

the battery died in my mouse right after that comment, sorry took forever to find a new one

- DanJS

\[x = \frac{ - (-6) \pm \sqrt{(-6)^2-4*1*13} }{ 2*1 }\]

- DanJS

\[x = \frac{ 6 \pm \sqrt{-16} }{ 2 }\]

- DanJS

the square root of a negative is not in the real numbers, for the complex, remember that the imaginary number i = square root of -1

- some.random.cool.kid

so so do i find the sqrt now because its 4

- DanJS

\[x = \frac{ 6 \pm \sqrt{16 * -1} }{ 2 } = \frac{ 6 \pm \sqrt{16}*\sqrt{-1} }{ 2 }\]

- DanJS

replace root of -1 with that imaginary I symbol , then just have to simplify by dividing 2 into the top , root 16 is 4

- some.random.cool.kid

i did say 4 its above

- DanJS

\[x = \frac{ 6 \pm 4*i}{ 2 } = 3 \pm 2i\]

- some.random.cool.kid

isnt that the simpliest of forms?

- some.random.cool.kid

so quick question do you have time for two more?

- DanJS

yeah, that is a conjugate pair, complex numbers come in pairs like that ..+ and -

- DanJS

x = 3 + 2i and x = 3 - 2i

- some.random.cool.kid

you've been the only great help today that was able to explain in manor that i understood hope you have more time for jus two more.

- DanJS

sure , i can spend like 10 min prolly

- some.random.cool.kid

great that should be enough. next one says -

- some.random.cool.kid

Solve the equation 4x2 + 8x + 1 = 0 by completing the square.
x equals start fraction three plus or minus square root of six end square root over two end fraction
x equals six plus or minus two square root of six end square root
x equals start fraction negative two plus or minus square root of three end square root over two end fraction
x equals start fraction four plus or minus three square root of six end square root over eight end fraction

- some.random.cool.kid

is this same method or is this the other method with teh factoring?

- DanJS

completing square, you want to turn the ax^2 + bx + c into something that will factor into (term)*(term) or (term)^2, which are sides of equal length of a square..

- DanJS

as now you cant...
4x^2 + 8x + 1 = 0

- DanJS

you can add something to both sides of the equations so that you find a value that will factor 4x^2 + 8x + c
The thing to remember is that you just take half of b^2

- DanJS

(b=8) [ b/2]^2 = [8/2]^2 = 16

- some.random.cool.kid

so 8/2^2?

- some.random.cool.kid

oh yeah

- DanJS

add 16 to both sides of the quadratic like this...
(4x^2 + 8x + 16) + 1 = 0 + 16

- DanJS

factorable now, and simplify

- DanJS

4(x^2 + 2x + 4) = 16 - 1

- some.random.cool.kid

mmm wait you had me and then lost me lol so what am i factoring the 16 8x and the other one if so how do i go about doing this, by finding the common multiple?

- DanJS

The reason to add (b/2)^2 = 16 to both sides, was because that will make the first two terms in the quadratic a perfect square with it... factors easy

- DanJS

see i added the 16 and grouped it with the 4x^2 + 8x + 16 ready to factor

- some.random.cool.kid

alright so...

- DanJS

4(x^2 + 2x + 4) = 16 - 1

- DanJS

x^2 + 2x + 4 = 15/4
(x + 2)*(x + 2) = 15/4

- some.random.cool.kid

15/4 = 3.75 correct?

- some.random.cool.kid

still there?

- some.random.cool.kid

mouse died again? lawl

- DanJS

no , messed up, answer was wrong... i see where now...
before you complete the square by adding on that half b squared term, you have to simplify the 4x^2 + 8x terms first by taking the factor of 4 out...

- DanJS

i will type it all

- DanJS

4x^2 + 8x + 1 = 0
4*(x^2 + 2x) + 1 = 0
x^2 + 2x = -1/4
now complete square

- DanJS

x^2 + 2x + 1 = -1/4 + 1
(x + 1)^2 = 3/4

- some.random.cool.kid

mmm ok

- some.random.cool.kid

is there something i should do next?

- some.random.cool.kid

dont leave ill be right back using the restroom real quick.

- DanJS

yeah take the square root of both sides, which recall has a + and a - value
then
subtract the 1 to isolate x

- DanJS

\[x+1 =\pm \sqrt{3/2} = \frac{ \pm \sqrt{3} }{ 2 }\]
\[x = \frac{ \pm \sqrt{3} }{ 2 } - 1\]

- some.random.cool.kid

ok

- some.random.cool.kid

whats next?

- DanJS

that is the answer, i was looking at the choices...
x equals start fraction negative two plus or minus square root of three end square root over two end fraction

- some.random.cool.kid

this should end with -2 + or minus sqrt of 3 all over two correct?

- some.random.cool.kid

oh nvm you just said that...

- DanJS

they wrote it as a single fraction, one last step i guess if you wanted....
replace the -1 with - 2/2

- DanJS

then combine into a single fraction

- some.random.cool.kid

k got it :D
this prob took longer than i thought sure you still have time for the last one?

- DanJS

cuz i f'ed up in like the first step.. hah

- some.random.cool.kid

lol

- DanJS

remember to put the thing into simler form next time before anything else

- some.random.cool.kid

ok

- DanJS

simplest form, standard form

- DanJS

sure , quickly,

- some.random.cool.kid

k great

- some.random.cool.kid

What are the zeros for the function f(x) = 3x2 + 2x + 2 and how many times does the graph cross the x-axis?
x equals start fraction negative one plus or minus i square root of seven end square root over three end fraction comma one time
x equals start fraction negative one plus or minus i square root of five end square root over three end fraction comma never
x equals start fraction negative two plus or minus two i square root of five end square root over three end fraction comma two times
x equals start fraction negative one plus or minus five i over three end fraction comma never

- some.random.cool.kid

i believe i got this one i thnk its d but it could also be the other never..

- some.random.cool.kid

my teach said it would be never but idk which one i figured the imaginary number but i might be wrong.

- DanJS

zeroes are x-intercept values, y = f(x) = 0
0 = 3x^2+2x+2

- some.random.cool.kid

ok

- DanJS

it is the second one ,
x equals start fraction negative one plus or minus i square root of five end square root over three end fraction comma never

- some.random.cool.kid

man so it was the second one darn knew it could figure out which one thanks i almost would have said the one because after i solved it i gave up on trying to figure out whether it was an imag or no...

- DanJS

that one you just hav eto put the numumbers into tha tquadratic formula for
a = 3
b=2
c=2

- some.random.cool.kid

thank you for your help and patience. night i am done with this review my next i dont think requires assistant so i will let you go now :~>

- DanJS

yeah no real zeros, just complex roots

- DanJS

complex zeros

- DanJS

k, i should be on here tomorrow , not sure

- some.random.cool.kid

:D i pasted all this as review for my EOC at the end of this semester well midterm ...

- some.random.cool.kid

ok thats perfect

- some.random.cool.kid

do you have an idea of what time tomorrow i have some more stuff thats related to this...

- some.random.cool.kid

i can hopefully use these as notes...

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