Question

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

Answer 1

please walk me thorugh...

Answer 2

through* to get the right answr. @Nnesha

Answer 3

@peachpi

Answer 4

@pooja195

Answer 5

@DanJS @Data_LG2 @dan815 @triciaal

Answer 6

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

Answer 7

i knew it but forgot mind showing me it?

Answer 8

If ax^2 + bx + c = 0

\[x = \frac{ -b \pm \sqrt{b^2-4ac} }{ 2a}\]

Answer 9

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

Answer 10

thank you*

Answer 11

oops i said b is bxD

Answer 12

i meant b is 6

Answer 13

a = 1
b = -6
c = 13

Answer 14

oops -6 not 6 ok

Answer 15

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

Answer 16

uh solve that?

Answer 17

want me to solve it?

Answer 18

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

Answer 19

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.

Answer 20

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

Answer 21

ok thank you

Answer 22

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

Answer 23

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

Answer 24

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

Answer 25

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

Answer 26

so so do i find the sqrt now because its 4

Answer 27

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

Answer 28

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

Answer 29

i did say 4 its above

Answer 30

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

Answer 31

isnt that the simpliest of forms?

Answer 32

so quick question do you have time for two more?

Answer 33

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

Answer 34

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

Answer 35

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.

Answer 36

sure , i can spend like 10 min prolly

Answer 37

great that should be enough. next one says -

Answer 38

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

Answer 39

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

Answer 40

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..

Answer 41

as now you cant...

4x^2 + 8x + 1 = 0

Answer 42

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

Answer 43

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

Answer 44

so 8/2^2?

Answer 45

oh yeah

Answer 46

add 16 to both sides of the quadratic like this...

(4x^2 + 8x + 16) + 1 = 0 + 16

Answer 47

factorable now, and simplify

Answer 48

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

Answer 49

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?

Answer 50

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

Answer 51

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

Answer 52

alright so...

Answer 53

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

Answer 54

x^2 + 2x + 4 = 15/4

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

Answer 55

15/4 = 3.75 correct?

Answer 56

still there?

Answer 57

mouse died again? lawl

Answer 58

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...

Answer 59

i will type it all

Answer 60

4x^2 + 8x + 1 = 0

4*(x^2 + 2x) + 1 = 0

x^2 + 2x = -1/4

now complete square

Answer 61

x^2 + 2x + 1 = -1/4 + 1

(x + 1)^2 = 3/4

Answer 62

mmm ok

Answer 63

is there something i should do next?

Answer 64

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

Answer 65

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

Answer 66

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

Answer 67

ok

Answer 68

whats next?

Answer 69

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

Answer 70

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

Answer 71

oh nvm you just said that...

Answer 72

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

Answer 73

then combine into a single fraction

Answer 74

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

Answer 75

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

Answer 76

lol

Answer 77

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

Answer 78

ok

Answer 79

simplest form, standard form

Answer 80

sure , quickly,

Answer 81

k great

Answer 82

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

Answer 83

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

Answer 84

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

Answer 85

zeroes are x-intercept values, y = f(x) = 0

0 = 3x^2+2x+2

Answer 86

ok

Answer 87

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

Answer 88

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...

Answer 89

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

Answer 90

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 :~>

Answer 91

yeah no real zeros, just complex roots

Answer 92

complex zeros

Answer 93

k, i should be on here tomorrow , not sure

Answer 94

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

Answer 95

ok thats perfect

Answer 96

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

Answer 97

i can hopefully use these as notes...