Question 60848
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help on this please,, thanks
x+1= sqrt(x+7)
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        The solution in the post by @jai_kos is incorrect.

        See my correct solution below.



x+1= sqrt(x+7)


Square on both sides, we get


(x+1)^2 = x +7
x^2 + 2x + 1 = x + 7


Reduce it to the standard form quadratic equation


x^2 + x - 6 = 0


Factor left side


(x+3)*(x-2) = 0


The roots of this equation are x = -3 and x = 2.
Direct check shows that x = 2 is the solution to the original equation, while x = -3 is an EXTRANEOUS solution.



<U>ANSWER</U>.  The given equation has a unique solution in real numbers x = 2.



Solved correctly.