2 Answers

BrilBroeder · Answer 1 · 2021-05-14T13:54:25+0000

Answer: "7 is a solution to the original equation. The value –1 is an extraneous solution."

Explanation:

The equation
x=√(6x+7) can be solved by squaring both sides:

$x^2 = 6x + 7\\\\x^2 - 6x - 7 = 0\\\\(x-7)(x+1) = 0$

We can see that -1 and 7 are solutions, but make sure they are not extraneous by substituting them in the original equation:

$1 = √(-1)\\ 7 = √(49)$

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."

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