math help: x times square root 7 + 4 = 2x (sqrt only on 7)

[shag1818]

i have a math problem due tomorrow and don't really know where to go with it.

The original problem was this:
x times the square root of 7 + 4 = 2x (sqrt only on the 7)

i believe you would get 2x - x*sqrt 7 = -4
then get x(2 - sqrt7) = -4
then you would get x = -4/2-sqrt7

I am not sure if i am right so far, but this is where i get confused. Does anyone have any hits for me so I can understand how to solve these types of problems?? Thanks in advance.

 

[jwpaine]

Hi.

You did everything right, accept you messed up on a sign when moving your 2x over.

x*sqrt(7)+4 = 2x

so -2x+x*sqrt(7) = -4

x(-2+sqrt(7))=-4
x = -4/(-2+sqrt(7))

See where you made your mistake?
Your answer is positive... mine is negative.

Cheers, and good job factoring out the x

John.

 

[shag1818]

one more question

thanks for the quick response. I do understand where I made the mistake.

One thing that i'm not sure of though is the answer i came up with. I don't think I can have a sqrt in the denominator, and in mine i have a sqrt 7 in it. Where would i go from there??? That is the part that is very confusing right now. Thanks again for catching the negative i forgot. I owe you

 

[jwpaine]

-4/(-2+sqrt(7))
is an acceptable answer...it's an irrational value.

Because 7 is a prime, you can't reduce sqrt(7) down any further.... it's right at home being part of your answer.


Hope this helps.
John.