Question

How do I do 2x^2=11x-5

Thanks!

Answer 1

I think I got it... is it -10?

Answer 2

We have
\[2x^2=11x-5\]
Do you know quadratic formula or do you know how to factor?

Answer 3

yes I know both

Answer 4

Nope, -10 is not the answer

Answer 5

Try again

Answer 6

Figured not. So I have to factor. I'll try tat.

Answer 7

10

Answer 8

So do I divide 2 on both sides and get x^2=5.5x-2.5

I think I messed up because I'm not sure how I would factor that.

Answer 9

I'll explain you
\[
2x^2=11x-5\]
Let's bring all the terms to one side
\[2x^2-11x+5=0\]
A standard quadratic is of the form
\[ax^2+bx+c=0\]
Tell me what's \( a\times b\) here?

Answer 10

Sorry a*c?

Answer 11

What's \(a \times c\) here?

Answer 12

2 times 5 would be ten then

Answer 13

I remember learning this, I hated it.

Answer 14

Yeah:)
What's b here?

Answer 15

11, right

Answer 16

It's very easy, After this you won't find trouble in solving these!!

Answer 17

I hope so since my final is soon (:

Answer 18

Uh-huh
We need the sign also

Answer 19

negative 11 then>

Answer 20

Yeah :)
Now I need you to split -11 into two numbers such that the product of the two numbers is 10 ( a*c)

Answer 21

Hmm... I'm not sure. Sorry, 5.5 is my only guess but I know that's not right.

Answer 22

I guess that would be -5.5

Answer 23

It's easy let the two numbers be x and y, we have two conditions
\[x+y=-11\]
and
\[x\times y=10\]
First factor 10 and you'll get an idea

Answer 24

I learned this as putting an equation that;s some thing like b=ax or some thing. But I'll try

Answer 25

Yeah , just find the two no.s and it's almost done

Answer 26

Will -1 and -10 work?

Answer 27

Ohhh

Answer 28

Sorry, I was drawing a blank.

Answer 29

So we stick those numbers some where... Into ax^2+bx+c ?

Answer 30

\[2x^2-11x+5=0\]
Now split -11x as -10x-1x
\[2x^2 -10x-1x+5=0\]

Answer 31

I never learned this way so sorry for my ignorance.

Answer 32

Now factoring is easy
\[2x^2 -10x-1x+5=0\]
\[2x( x-5)-1(x-5)=0\]
Now take (x-5) common, we get
\[(x-5)(2x-1)=0\]
Do you get this?

Answer 33

It's fine:)

Answer 34

So those are treated as two seperate things and factored semperately. SOrry for my typing, bad keyboard

Answer 35

Yeah:) Can you find the values of x ?

Answer 36

Not sure how to unless I decided to guess and check.):

Answer 37

@randomemail98 I gotta go now, Sorry
My friends will help you out
@ParthKohli @Callisto Please help

Answer 38

Alright bud

Answer 39

Thank you so far

Answer 40

Now, do you know the zero product rule?

Answer 41

That a quadratic has to equal zero? If that's not it, then no.

Answer 42

Okay, see :)
Whenever (x - a)(x - b) [this is the factored quadratic expression] equals zero, then either x - a is 0, or x - b is 0.

Answer 43

Now think of it like this. Whenever you multiply anything by 0, you get 0. Here, one of the numbers MUST be zero to make it 0.

Answer 44

Yes, that makes sense

Answer 45

The question is asking for 1 integer by the way

Answer 46

Now, the factored form is \((x + 5)(2x + 1)\)
Either x + 5 = 0 or 2x + 1 = 0

\( \color{Black}{\Rightarrow x + 5 = 0 }\)

\( \color{Black}{\Rightarrow 2x + 1 = 0 }\)

One of them doesn't have an integer as the solution.

Answer 47

It says The integer is _____
Please don;t tell me I didn;t have to solve it or some thing, man. D:

Answer 48

2x^2=11x-5 2x^2 -11x +5 =0 (2x-1)(x-5)=0

Answer 49

its -11

Answer 50

Callisto is smart lol

Answer 51

Whenever you have \( \color{Black}{(x + a)(x + b) = 0 }\), then you make two different equations like this.

\( \color{Black}{\Rightarrow x + a = 0 }\)
\( \color{Black}{\Rightarrow x + b }\)

This makes you determine the values.

Answer 52

As it is \( \color{Black}{\Rightarrow (2x - 1)(x - 5) = 0 }\)
Two equations:

\( \color{Black}{\Rightarrow 2x - 1 = 0 }\)
\( \color{Black}{\Rightarrow x - 5 = 0 }\)

Solving,
\( \color{Black}{\Rightarrow 2x = 1 }\)
\( \color{Black}{\Rightarrow x = 0.5 }\)

We're not done.

\( \color{Black}{\Rightarrow x - 5 = 0 }\)
\( \color{Black}{\Rightarrow x = 5 }\)
:)

Answer 53

The integer solution I see here is x = 5

Answer 54

So oe of you say -11 and one say 5... D:

Answer 55

Callisto, tell who's correct :D

Answer 56

@randomemail98 It's 5 ... '-11' means it's '-11x' in the question..

Answer 57

Oh, I think I get it now. I;ve never seen it like that, but it's a good method. Thanks you guys, you didn;t have to all come here :P

Answer 58

I'm gonna close this, thanks you all!