Question 640044
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In the future, use sqrt(*expression*) to indicate square root.  Use either sqrt[n](x) or root(x,n) to indicate *[tex \LARGE \sqrt[n]{x}]


The first thing is that you don't want to have two terms with a radical on one side of an equation if you can help it.  In this case, add *[tex \LARGE -\sqrt{x}] to both sides of the equation:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sqrt{x\ -\ 6}\ =\ 6\ -\ \sqrt{x}]


Square both sides


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ -\ 6\ =\ 36\ -\ 12\sqrt{x}\ +\ x]


Rearrange, collect terms, etc.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 12\sqrt{x}\ =\ 42]


Multiply both sides by *[tex \LARGE \frac{1}{12}] and then reduce the fraction in the RHS.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sqrt{x}\ =\ \frac{42}{12}\ =\ \frac{7}{2}]


Square both sides:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{49}{4}]


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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