# Thread: Show how to solve for x

1. ## Show how to solve for x

x/6 = 6/x-8 Answer is x = 4 + 2 times the square root of 13, but I don't know how to derive it

2. Originally Posted by Chuck
x/6 = 6/x-8 Answer is x = 4 + 2 times the square root of 13, but I don't know how to derive it
Multiply both sides by $x$ to get:
$\frac{1}{6}x^2 = 6 - 8x$

Which implies that
$\frac{1}{6}x^2 + 8x - 6 = 0$

3. Gack! "Last" is sleeping on the job.

1) Please don't EVER casually multiply by 'x' wihtout at least considering the consequences. If x = 0, you are in big trouble!

2) Please write more carefully. Remember your Order of Operations. You have not written what you intended. You meant this:

x/6 = 6/(x-8)

Look at this and what you wrote and see the difference.

$
\frac{x}{6} = \frac{6}{x-8}
$

#1 Notice that x = 8 is no good. Why? No matter what else happens, do NOT believe that x = 8.

Having said that, multiply both sides by 'x-8'. This gives:

$
\frac{x \cdot (x-8)}{6} = 6
$

Multiply both sides by 6. Why was there no additional consideration this time? We know already that 6 is NOT zero (0).

Now we have:

$
x \cdot (x-8) = 36
$

or

$
x^{2}-8x = 36
$

or

$
x^{2}-8x - 36 = 0
$

And that should be familar and suggest, if nothing else, Completing the Square or the Quadratic Formula.

4. Originally Posted by Chuck
x/6 = 6/x-8
That's what the OP provided. I interpreted it as $x/6 = 6/x - 8$. If he meant $x/6 = 6/(x-8)$, he would have put the parenthesis there.

And from that, it is implied that $x \neq 0$. Otherwise the $6/x$ would be undefined.

Whatever.

5. Originally Posted by Last_Singularity
That's what the OP provided. I interpreted it as $x/6 = 6/x - 8$. If he meant $x/6 = 6/(x-8)$, he would have put the parenthesis there.
as it turns out, a lot of people don't know how to use parentheses and would not type them even if that's what they mean.

no worries, you did what you could, it is up to the OP to clarify what they mean. if there are any doubts, just ask before posting