Question 358678
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \sqrt{3x\ +\ 7}\ -\ 3]


If possible, get the radical by itself on one side of the equation:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ +\ 3\ =\ \sqrt{3x\ +\ 7}]


Now square both sides:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ 6x\ +\ 9\ =\ 3x\ +\ 7]


Collect like terms and put the quadratic into standard form:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ 3x\ +\ 2\ =\ 0]


Now just factor your quadratic and solve.  As usual with quadratics you will get two roots.  Check both of them in the original equation to ensure that you didn't introduce an extraneous root in the process of squaring when you solved the equation.


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