Question

Solve for x : √8-2x=x+4

Answer 1

So the radical is just over the 8?

Answer 2

\[\sqrt{8}-2x=x+4? \]
\[\sqrt{8-2x}=x+4 ?\]

Answer 3

no its the second one

Answer 4

Have you tried squaring both sides to get rid of the radical?

Answer 5

I have no clue how to do that

Answer 6

\[\text{ for example, we want to solve this one: } \sqrt{x}=9\]
We square both sides
\[(\sqrt{x})^2=(9)^2\]
\[x=81 \]

Answer 7

So you try squaring both sides for the one above

Answer 8

uhh I have no clue , it sounds about right though

Answer 9

Ok so when you have squared both sides you can draw it if you want what you will get after doing so

Answer 10

So what did you get after squaring both sides?

Answer 11

Here is another example
Pretend we want to solve:
\[\sqrt{x-2}=x+4\]
We square both sides to get rid of the radical
\[(\sqrt{x-2})^2=(x+4)^2\]
\[(x-2)=(x+4)^2\]
\[x-2=(x+4)^2\]
Now remember the objective is to solve for x
But we need to multiply that one squared junk out
\[x-2=(x+4)(x+4)\]
\[x-2=x^2+4x+4x+16\]
\[x-2=x^2+8x+16\]
Now this is a quadratic and I would put it in this form \[ax^2+bx+c=0 \text{ and use the quadratic formula } x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \text{ to solve }\]

Answer 12

Ohhh , okay . so If I were to square both sides I would get (√8-2x)^2=(x-4)^2 ?

Answer 13

And then 8-2x = x-4 ?

Answer 14

well what happened to the square on the right hand side?

Answer 15

ohh okay . so uhh 8-2x = (x-4) (x-4) right ?

Answer 16

right! :)

Answer 17

wait what happen to the plus

Answer 18

in the orginal equation you had x+4 not x-4

Answer 19

I just looked back at my probllem in my homework & I mistyped it , its actually x-4

Answer 20

ok

Answer 21

So thats it to the problem ? did I answer it ?

Answer 22

No you have to solve for x

Answer 23

Do you see in my example?
The next step after what you have was to multiply (x-4)(x-4) out

Answer 24

then I said to put in this form:
\[ax^2+bx+c=0\]
so you can use the quadratic formula

Answer 25

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

Answer 26

That would be solving it for x because x is by itself

Answer 27

Okay so my next step would be to 8-2=x^2-4x-4x-16 ?

Answer 28

\[8-2x=x^2-4x-4x+16 \]

Answer 29

oh snap , I was close ! lol okay so then it would be 8-2=x^2-8x+16 right ?

Answer 30

you keep leaving that other x out
but the other side is peachy! :)

Answer 31

8-2x=x^2-8x+16

Answer 32

Now subtract/add to both sides to put everything on one side

Answer 33

You want everything on one side while 0 is on the other

Answer 34

Ohh okay .. so what would i add or subtract first ;o

Answer 35

No matters
You just want everything on one side

Answer 36

I got x^2+6x-8 , is that correct ?

Answer 37

\[8-2x=x^2-8x+16 \]
So I want everything on one side
So I'm gonna add 2x on both sides
And
I'm gonna subtract 8 on both sides
-8 +2x +2x -8
-----------------------
\[0=x^2-8x+2x+16-8\]
\[0=x^2-6x+8\]
Very close! :)

Answer 38

Now you are almost done
You could use the quadratic formula or try to factor (there is also completing the square but lets not-lol)
Hint: factoring would work out nicely here actually

Answer 39

Do you know how to factor?

Answer 40

I think is it where you have to find to numbers that will multiply & add into the two numbers ?

Answer 41

multiply to 8
and
add to -6
:)

Answer 42

4 & 2

Answer 43

how about -4 and -2

Answer 44

-4(-2)=8
-4+(-2)=-6

Answer 45

so
0=(x-4)(x-2)
:)
Now set both factors =0

Answer 46

But hey @breeskee03 you need to be careful
about your solutions here

Answer 47

because 8-2x has to be positive in order for there to be a solution

Answer 48

So let me know what you get after solving 0=(x-4)(x-2)
then I will go further with you okay?

Answer 49

SO I plug it in now ?

Answer 50

Set both factors =0
x-4=0 or x-2=0
Now solve both of these
And then after you get those make sure when you plug into your original equation they both work

Answer 51

You should be able to add 4 on both sides for x-4=0

And

You should be able to add 2 on both sides for x-2=0

Answer 52

okay (: Thank you so much !

Answer 53

You got it?

Answer 54

Thanks for working so hard to understand. I really like that about students. I'm proud of you for getting through this question. Go you! :)