Question 343483
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I presume that you want to solve this equation for *[tex \Large x], although you might have shown us a mocodium of courtesy by taking a scant few seconds to say so.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sqrt{3x\ +\ 7}\ =\ 3x\ +\ 5]


Square both sides:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3x\ +\ 7\ =\ 9x^2\ +\ 30x\ +\ 25]


Collect like terms on the left:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 9x^2\ +\ 27x\ +\ 18\ =\ 0]


Divide by 9:


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


Solve the factorable quadratic for *[tex \Large x].


Check both roots to make sure you did not introduce an extraneous root in the process of squaring the equation in the first step.


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