Answer: "7 is a solution to the original equation. The value –1 is an extraneous solution."
Step-by-step explanation:
The equation [tex]x=\sqrt{6x+7}[/tex] can be solved by squaring both sides:
[tex]x^2 = 6x + 7\\\\x^2 - 6x - 7 = 0\\\\(x-7)(x+1) = 0[/tex]
We can see that -1 and 7 are solutions, but make sure they are not extraneous by substituting them in the original equation:
[tex]1 = \sqrt{-1}\\ 7 = \sqrt{49}[/tex]
The square root of 49 equals 7, but the square root of -1 is an imaginary number.
The correct choice is "7 is a solution to the original equation. The value –1 is an extraneous solution."
