Show all work to solve the equation for x. If a solution is extraneous, be sure to identify it in your final answer.

square root of the quantity x plus 6 end quantity minus 4 equals x

Question

Show all work to solve the equation for x. If a solution is extraneous, be sure to identify it in your final answer.

square root of the quantity x plus 6 end quantity minus 4 equals x

Timmyspu · Answer

Do you have a screenshot? That would help a lot if you did.

kekeman · Answer

https://snipboard.io/fKkWoT.jpg

Timmyspu · Answer

Ok, there is steps to do this equation. So do you know how to do the first step for this equation?

kekeman · Answer

Yes i did the whole first part: https://snipboard.io/pIlFbw.jpg But i don't know how to do the ending part

kekeman · Answer

I am having trouble with the ending i am getting kinda confused

Timmyspu · Answer

It looks like you got the answer. All you need to remove is the +  and then your answer should be 0=x^2

kekeman · Answer

No everyone is saying the answer is x=2 but i am trying to figure out how to get that

kekeman · Answer

https://snipboard.io/aivbNK.jpg

Timmyspu · Answer

What you should do different is you got rid of the ^2 and you should have just kept it out and I am a little confused why you just put it back in because it just looked like you just pulled it from the middle of no where.

kekeman · Answer

The last line i was not down completing it so i just stopped because i was getting confused on what the next step was

Timmyspu · Answer

The very last step was just your answer. All you had to do was just take

x^2 and just put it as X times X and then you just make it 2x and then you just go from there.

kekeman · Answer

So the final answer is 2?

kekeman · Answer

I am super confused rn

kekeman · Answer

x = 2?

Timmyspu · Answer

I dont know right now I am out of it right now I have not slept very much so @vocaloid can explain this better than me. I believe x=2 should be your answer.

kekeman · Answer

Mmmm okii

Vocaloid · Answer

You expanded (x+4)(x+4) incorrectly

(x+4)(x+4) = x^2 + 8x + 16 (FOIL)

Now:

x + 6 = x^2 + 8x + 16

Subtract x + 6 from both sides

x^2 + 7x + 10 = 0

Factor

(x+5)(x+2) = 0

Now,

(x + 5) = 0 and (x + 2) = 0 are possible solutions meaning x = -5 or x = -2

However you cannot just stop there. If you plug in x = -5 you get

Sqrt(x + 6) = x -+ 4

Sqrt(1) = -1 which is not true. This makes x = -5 extraneous. Therefore x = -2 is your only solution

kekeman · Answer

Okkk well i'm confused on why it keeps saying positive 2

kekeman · Answer

Nvm you are very right i was putting the whole equation under the square

kekeman · Answer

Thanks for the help