Question

Solve for x: please show work :)
8=19x-2x^2

Answer 1

Step 1: Factor out the x first
Please do so. :)

Answer 2

can you tell me how to do that?

Answer 3

\[8=19x-2x^2\]
\[2x^2-19x+8=0\] is a start

Answer 4

Or yes, can take it Satellite the Legend's way

Answer 5

ok

Answer 6

what?

Answer 7

then use the quadratic formula

Answer 8

I'm not sure what that is

Answer 9

you cannot factor this using whole numbers

Answer 10

either of those things

Answer 11

i've never actually done this before

Answer 12

Satellite...wouldn't that just result in a more complex thing?
If you factor the x out, or you simply factor the way you said it...it would be more simpler i believe.

Answer 13

uk

Answer 14

then your are in a bit of trouble
the solutions to \[ax^2+bx+c=0\] are \[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]

Answer 15

ok, this is like hieroglyphics to me

Answer 16

@karatechopper no you can't do that
that is why you need the quadratic formula

Answer 17

ok. i'm lost

Answer 18

lets go slow

Answer 19

is there a way you can show me instead? I don't know these terms

Answer 20

this is your original equation \[8=19x-2x^2\] right?

Answer 21

oh wait, i get it. He's right.
LIKE ALWAYS.

Answer 22

yes

Answer 23

what now?

Answer 24

k
the first thing we are going to do is set it equal to zero
by adding \(2x^2\) to both sides, and subtracting \(19x\) from both sides to start with
\[2x^2-19x+8=0\] ok with that step?

Answer 25

yep

Answer 26

i wrote that down. what next?

Answer 27

the next thing is to realize that this looks just like a general quadratic equation
\[ax^2+bx+c=0\] with
\[a=2,b=-19,c=8\]
is that ok?

Answer 28

ok

Answer 29

the general solutions to
\[ax^2+bx+c=0\] are
\[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]

Answer 30

woe

Answer 31

that is called the "quadratic formula" and you can't avoid it, you have to use it
i will walk you through it

Answer 32

oh. thanku

Answer 33

\[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]
\[a=2,b=-19,c=8\] we make a direct substitution and get
\[x=\frac{-(-19)\pm\sqrt{(-19)^2-4\times 2\times 8}}{2\times 2}\]
let me know when you get what i wrote

Answer 34

got it

Answer 35

it is arithmetic from here on in

Answer 36

i just did it way wrong

Answer 37

i wrote that down

Answer 38

and must be missing something

Answer 39

you get
\[x=\frac{19\pm\sqrt{19^2-64}}{4}\] as a start

Answer 40

ok...

Answer 41

then since \(119^2-64=297\) you get
\[x=\frac{19\pm\sqrt{297}}{4}\]

Answer 42

i don't know what the + sign means when its underlined

Answer 43

two answers
plus or minus

Answer 44

just like if you have
\[x^2=25\] then \(x=\pm5\) it is an abbreviation for \(x=5\) or \(x=-5\)

Answer 45

ohhhh. that explains alot. ha

Answer 46

ok got it

Answer 47

how dp i know when i'm done?

Answer 48

when you get
\[x=\frac{19\pm\sqrt{297}}{4}\] or if you prefer
\[x=\frac{19\pm3\sqrt{33}}{4}\]

Answer 49

oh, ok. i see. I'm extreme newby

Answer 50

thank you! that was a great understandable explanation . much appreciated!

Answer 51

yw

Answer 52

Do you know how I can ask a grid question?

Answer 53

?

Answer 54

without having a grid to show

Answer 55

one question is telling u to graph a line, and the other is showing you coordinates on a grid and asking for the slope

Answer 56

oh, I c attach file