Question 322979
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Presuming you mean:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sqrt{9x\ +\ 55}\ =\ x\ +\ 5]


which makes sense, instead of 


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sqrt{9x}\ +\ 55\ =\ x\ +\ 5]


which is really what you wrote, proceed as follows:


Square both sides:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 9x\ +\ 55\ =\ x^2\ +\ 10x\ +\ 25]


Collect everything on the left:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ x\ -\ 30\ =\ 0]


Which is an easily factorable quadratic (6 plus -5 = 1, 6 times -5 equals -30).


<i>Check <b>both</b> roots.  One of them will <b>not</b> check.  Exclude that root as extraneous -- introduced by squaring both sides of the equation in the first step.</i>


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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