Question

hot to convert the equation -x^2+3=(4x-1)^2 into ax^2+bx+c=0 form

Answer 1

first step: simplify (4x-1)^2

Answer 2

k so it would be 1 or 16x-1?

Answer 3

ugh im so confused:l

Answer 4

are you talking about the answer?

Answer 5

yeah, i wanna put the equation into standard form but i have no idea how

Answer 6

well like i said you have to expand (4x-1)^2 first...what is the expansion of this?

Answer 7

16x-1?

Answer 8

i dont know what to do after you get
-x^2+3=16x-1

Answer 9

it's not 16x -1

Answer 10

aah okay, so what is it?

Answer 11

(x+1)^2 = (x+1)(x+1) = x^2 + x + x + 1 = x^2 + 2x + 1

(x+2)^2 = (x+2)(x+2) = x^2 + 2x + 2x + 4 = x^2 + 4x + 4

(x-3)^2 = (x-3)(x-3) = x^2 - 3x - 3x + 9 = x^2 - 6x + 9

so what does (4x-1)^2 equal to?

Answer 12

i have no idea how you even did any of those equations

Answer 13

r u sure this is how you put the equation into ax^2+bx+c+0?

Answer 14

yep

Answer 15

\[\huge (4x-1)^2 \implies (4x-1)(4x-1)\]
now use FOIL on (4x-1)(4x-1)

Answer 16

all ik from an example is 0x^2+3=(2x-1)^2 converted is 5x^2-4x-2=0

Answer 17

did you write something wrong there?

Answer 18

so how is that supposed to help me?

Answer 19

insted of a 0 it was supposed to be - sorry

Answer 20

hmm okay...how about i show you how they got that...maybe you'll get an idea

Answer 21

ok, thankyou sooooo much!

Answer 22

i know how they got eveything in the equation except the 5x^2 part

Answer 23

\[-x^2 +3 = (2x-1)^2\]
expand (2x-1)^2 first
\[(2x-1)^2 \implies (2x-1)(2x-1) \implies 4x^2 - 2x - 2x + 1 \implies 4x^2 - 4x + 1\]

so the equation a while ago becomes
\[-x^2 + 3 = 4x^2 - 4x + 1\]
add x^2 to both sides
\[3 = 5x^2 - 4x + 1\]
now subtract 3 from both sides
\[0 = 5x^2 - 4x - 2\]

Answer 24

does that help?

Answer 25

ummm one sec

Answer 26

sure

Answer 27

so the answer to -x^2+3=(4x-1)^2 is 17x^2-8x-3=0?

Answer 28

very close...except for -3...recheck your work

Answer 29

kk

Answer 30

17x^2-8x-2???

Answer 31

yup

Answer 32

YES! thank you so much:)

Answer 33

welcome ^_^

Answer 34

caaaann i ask another question?

Answer 35

sure

Answer 36

how would you find the solutions to the equation 2x^2+5x+8=5?

Answer 37

would you convert it to 2x^2+5x+3=0 first?

Answer 38

yep. then you factor if possible

Answer 39

ok sooo how do you do that? haha u probs think im hella stupid:P

Answer 40

nahh

Answer 41

if you're not used to factoring you can just use quadratic formula \[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]
do you know how to use it?

Answer 42

yeah

Answer 43

great. so use it. then tell me what you get

Answer 44

okay soooo -3 and 2?

Answer 45

haha im thinkin its wrong

Answer 46

hmm...yeah..it is...

Answer 47

ooh wait, sorry wrong problem i actually need to do x^2+20=-9x

Answer 48

hint:
a = 2
b= 5
c = 3
\[x = \frac{-5 \pm \sqrt{5)^2 - 4(2)(3)}}{2(2)}\]

Answer 49

lol

Answer 50

find the solutions?

Answer 51

so it would be -4 and -5?

Answer 52

haha yeah im not the brightest at math:)

Answer 53

yup -4 and -5

x^2 + 9x + 20 = 0
(x+5)(x+4) = 0
so roots are x = -5 and x = -4

Answer 54

so insted of doing the super long way you can just find the lowest factors of 20?

Answer 55

haha yup...but expressions arent always facorable...and finding the factors isnt that easy either

Answer 56

darn:l

Answer 57

are you like a teacher or somthin?

Answer 58

close to that haha

Answer 59

haha close?

Answer 60

yeah..something like that =))

Answer 61

lol gotcha

Answer 62

another question?

Answer 63

go for it

Answer 64

what number would you add to complete the square for the equation
x^2+6x=0

Answer 65

do you know how to complete the square?

Answer 66

no idea haha

Answer 67

hmm that's okay...can you identify what the COEFFICENT of x is?

Answer 68

1?

Answer 69

1 is the coefficient of x^2...im asking he coefficient of x

Answer 70

ooh 6?

Answer 71

right. now divide it by 2

Answer 72

3

Answer 73

now square it

Answer 74

12

Answer 75

nooo

Answer 76

hehe

Answer 77

9

Answer 78

wait is it seriously that easy????

Answer 79

haha yea im a weird one:)

Answer 80

yup

Answer 81

wow

Answer 82

i mean yes it is seriously that easy...not that your a weird one

Answer 83

so then how would you do x^2+12x=9?

Answer 84

how would you?

Answer 85

haha nah i didnt say wow cuz of the yup i ment wow cuz it was that easy

Answer 86

to complete the square

Answer 87

oh...the whole process?

Answer 88

yes pleasseee

Answer 89

so what will you add to both sides?

Answer 90

add?

Answer 91

like the question earlier

Answer 92

the question a while ago was

what number would you add to complete the square for the equation
x^2+6x=0

this time it's

what number would you add to complete the square for the equation
x^2+12x = 9

Answer 93

ooh so it would be 36?

Answer 94

yup so add 36 to BOTH sides

x^2 + 12x + 36 = 9 + 36

simplify it

Answer 95

x^2+12x-9=0?

Answer 96

how would you complete the square for 2x^2-28x-2=-50 and then solve for x?