You can put this solution on YOUR website! x+1= sqrt x+7
Square on both sides, we get
(x+1)^2 = x +7
x^2 + x + 1 = x + 7
Get all the numbers on one side and “x” to the other side
x^2 + x – x = 7 -1
x^2 = 6
Take the sqrt of the equation, we get
x = sqrt(6)
Hence the value of “x” = sqrt(6)
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.
ANSWER. The given equation has a unique solution in real numbers x = 2.
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