Question

Solve for all possible values of x. x^2 + 4x -21=0.

Answer 1

(x-3)(x+7)

Answer 2

dont forgot a medal

Answer 3

How did you get that?

Answer 4

foil

Answer 5

x*x = x^2

Answer 6

7x+-3x

Answer 7

-3 * 7

Answer 8

x_1 =3
x_2= -7

Answer 9

Im still confused.. How do you convert the problem to the ( )? I get the whole x thing, but wht about the 4 & -21?

Answer 10

you can factorizing this equation in the form (x-3)(x+7) and now you see that this is equal zero when one of this factors is equal zero so (x-3)=0 or (x+7)=0
and now when x-3=0 result x=3 and from x+7=0 result x=-7
- hope so much that now you can understanding all this work

Answer 11

Okay.. how do you factorize? And how do you solve after getting it in the ( )?

Answer 12

its a sort of confusing problem there are more than 1 ways to solve it u might one to read your textbook or ask your teacher and they tell and explain easiest way

Answer 13

dont forget medal for advice

Answer 14

Its summer homework, i dont have a teacher or a textbook. -.-

Answer 15

try youtube

Answer 16

they have videos of teachers doing it

Answer 17

type in the topic like : "how to add decimals" and a video will come up

Answer 18

Mkay, sounds easy enough.

Answer 19

when you have x^2 + 4x -21=0, you try to find two numbers, which if you add together you get 4, and if you multiply together you get -21. The numbers are -3 and 7, so you put them in brackets: (x-3)(x+7)

Answer 20

Your Welcome and good luck.

Answer 21

dont foget the medal

Answer 22

then you equate (x-3) = 0 - you get x=3, and then (x+7)=0, you get x=-7. So 3 and -7 are the two roots...

Answer 23

So the answer is just what the numbers that go into the other numbers are?

Answer 24

You start off with \(x^{2} + 4x - 21\). What you want to do is find two numbers which will \(\textit{multiply}\) to get you -21, and which will \(\textit{add}\) to get you +4. In this case, you would take the numbers +7, and -3 (notice how \(7 \times -3 = -21\) and \(7-3=4\)). Then you break up the original question a little bit:
\[x^2 + 4x - 21 = x^2 + 7x -3x -21\], notice that I turned the 4x into 7x - 3x.
Then take the x out of the first two: \[x^2+7x-3x-21 = x(x + 7) - 3x -21\]. That \((x+7)\) is your first factor. The other one is \((x-3)\), since the other x has a -3 in front of it. So you end up with \((x+7)(x-3)\)

Answer 25

you need to know from your math studies that x_1 + x_2 = -b/a and x_1 * x_2 = c/a and now if you see in your equation there is x_1 + x_2 = 4 and x_1 * x_2 = -21 after this you see that for 3 and -7 there you will get exactly this results

Answer 26

I don't really understand you, but I think the answer is yes - only that the sign is different. Since you get (x-3) and (x+7), you must equate each one of them to zero. You will get 3 and -7, NOT 3 and -7

Answer 27

So you just switch the signs? Will it work in any equation like this?

Answer 28

It will only work when it's x^2 plus something x + something. NOT when it's 2x^2 + something or 3x^2, or so on.

Answer 29

Oh! okay, thankyou.