some.random.cool.kid
  • some.random.cool.kid
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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some.random.cool.kid
  • some.random.cool.kid
please walk me thorugh...
some.random.cool.kid
  • some.random.cool.kid
through* to get the right answr. @Nnesha
some.random.cool.kid
  • some.random.cool.kid
@peachpi

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More answers

some.random.cool.kid
  • some.random.cool.kid
@pooja195
some.random.cool.kid
  • some.random.cool.kid
@DanJS @Data_LG2 @dan815 @triciaal
DanJS
  • DanJS
you know the quadratic formula that results from solving that standrard quadratic form for x =
some.random.cool.kid
  • some.random.cool.kid
i knew it but forgot mind showing me it?
DanJS
  • DanJS
If ax^2 + bx + c = 0 \[x = \frac{ -b \pm \sqrt{b^2-4ac} }{ 2a}\]
some.random.cool.kid
  • 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
  • some.random.cool.kid
thank you*
some.random.cool.kid
  • some.random.cool.kid
oops i said b is bxD
some.random.cool.kid
  • some.random.cool.kid
i meant b is 6
DanJS
  • DanJS
a = 1 b = -6 c = 13
some.random.cool.kid
  • some.random.cool.kid
oops -6 not 6 ok
DanJS
  • DanJS
x^2 + (-6)x .....
some.random.cool.kid
  • some.random.cool.kid
uh solve that?
some.random.cool.kid
  • some.random.cool.kid
want me to solve it?
DanJS
  • DanJS
yeah , use those values and simplify as much as you can
some.random.cool.kid
  • 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
  • DanJS
ill type it out fast, i have to run for a while ... one sec
some.random.cool.kid
  • some.random.cool.kid
ok thank you
DanJS
  • DanJS
the battery died in my mouse right after that comment, sorry took forever to find a new one
DanJS
  • DanJS
\[x = \frac{ - (-6) \pm \sqrt{(-6)^2-4*1*13} }{ 2*1 }\]
DanJS
  • DanJS
\[x = \frac{ 6 \pm \sqrt{-16} }{ 2 }\]
DanJS
  • 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
  • some.random.cool.kid
so so do i find the sqrt now because its 4
DanJS
  • DanJS
\[x = \frac{ 6 \pm \sqrt{16 * -1} }{ 2 } = \frac{ 6 \pm \sqrt{16}*\sqrt{-1} }{ 2 }\]
DanJS
  • 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
  • some.random.cool.kid
i did say 4 its above
DanJS
  • DanJS
\[x = \frac{ 6 \pm 4*i}{ 2 } = 3 \pm 2i\]
some.random.cool.kid
  • some.random.cool.kid
isnt that the simpliest of forms?
some.random.cool.kid
  • some.random.cool.kid
so quick question do you have time for two more?
DanJS
  • DanJS
yeah, that is a conjugate pair, complex numbers come in pairs like that ..+ and -
DanJS
  • DanJS
x = 3 + 2i and x = 3 - 2i
some.random.cool.kid
  • 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
  • DanJS
sure , i can spend like 10 min prolly
some.random.cool.kid
  • some.random.cool.kid
great that should be enough. next one says -
some.random.cool.kid
  • 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
  • some.random.cool.kid
is this same method or is this the other method with teh factoring?
DanJS
  • 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
  • DanJS
as now you cant... 4x^2 + 8x + 1 = 0
DanJS
  • 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
  • DanJS
(b=8) [ b/2]^2 = [8/2]^2 = 16
some.random.cool.kid
  • some.random.cool.kid
so 8/2^2?
some.random.cool.kid
  • some.random.cool.kid
oh yeah
DanJS
  • DanJS
add 16 to both sides of the quadratic like this... (4x^2 + 8x + 16) + 1 = 0 + 16
DanJS
  • DanJS
factorable now, and simplify
DanJS
  • DanJS
4(x^2 + 2x + 4) = 16 - 1
some.random.cool.kid
  • 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
  • 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
  • DanJS
see i added the 16 and grouped it with the 4x^2 + 8x + 16 ready to factor
some.random.cool.kid
  • some.random.cool.kid
alright so...
DanJS
  • DanJS
4(x^2 + 2x + 4) = 16 - 1
DanJS
  • DanJS
x^2 + 2x + 4 = 15/4 (x + 2)*(x + 2) = 15/4
some.random.cool.kid
  • some.random.cool.kid
15/4 = 3.75 correct?
some.random.cool.kid
  • some.random.cool.kid
still there?
some.random.cool.kid
  • some.random.cool.kid
mouse died again? lawl
DanJS
  • 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
  • DanJS
i will type it all
DanJS
  • DanJS
4x^2 + 8x + 1 = 0 4*(x^2 + 2x) + 1 = 0 x^2 + 2x = -1/4 now complete square
DanJS
  • DanJS
x^2 + 2x + 1 = -1/4 + 1 (x + 1)^2 = 3/4
some.random.cool.kid
  • some.random.cool.kid
mmm ok
some.random.cool.kid
  • some.random.cool.kid
is there something i should do next?
some.random.cool.kid
  • some.random.cool.kid
dont leave ill be right back using the restroom real quick.
DanJS
  • DanJS
yeah take the square root of both sides, which recall has a + and a - value then subtract the 1 to isolate x
DanJS
  • DanJS
\[x+1 =\pm \sqrt{3/2} = \frac{ \pm \sqrt{3} }{ 2 }\] \[x = \frac{ \pm \sqrt{3} }{ 2 } - 1\]
some.random.cool.kid
  • some.random.cool.kid
ok
some.random.cool.kid
  • some.random.cool.kid
whats next?
DanJS
  • 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
  • some.random.cool.kid
this should end with -2 + or minus sqrt of 3 all over two correct?
some.random.cool.kid
  • some.random.cool.kid
oh nvm you just said that...
DanJS
  • DanJS
they wrote it as a single fraction, one last step i guess if you wanted.... replace the -1 with - 2/2
DanJS
  • DanJS
then combine into a single fraction
some.random.cool.kid
  • 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
  • DanJS
cuz i f'ed up in like the first step.. hah
some.random.cool.kid
  • some.random.cool.kid
lol
DanJS
  • DanJS
remember to put the thing into simler form next time before anything else
some.random.cool.kid
  • some.random.cool.kid
ok
DanJS
  • DanJS
simplest form, standard form
DanJS
  • DanJS
sure , quickly,
some.random.cool.kid
  • some.random.cool.kid
k great
some.random.cool.kid
  • 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
  • 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
  • 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
  • DanJS
zeroes are x-intercept values, y = f(x) = 0 0 = 3x^2+2x+2
some.random.cool.kid
  • some.random.cool.kid
ok
DanJS
  • 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
  • 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
  • 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
  • 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
  • DanJS
yeah no real zeros, just complex roots
DanJS
  • DanJS
complex zeros
DanJS
  • DanJS
k, i should be on here tomorrow , not sure
some.random.cool.kid
  • 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
  • some.random.cool.kid
ok thats perfect
some.random.cool.kid
  • 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
  • some.random.cool.kid
i can hopefully use these as notes...

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