Decide what values of the variable cannot possibly be solutions for the equation.
-$$\sqrt { x + 7 } + 5 = x$$
A) {2, 9}
B) {2}
C) {9}
D) {9, 18}

Question

Quizplus · Accepted Answer

The equation $\sqrt { x + 7 } + 5 = x$ implies that $x$ must be greater than or equal to -7, because the square root of a negative number is not real. Solving the equation by squaring both sides gives $x + 7 + 10\sqrt{x + 7} + 25 = x^2$, which simplifies to a quadratic equation. However, the critical insight is that the original equation has a constraint due to the square root. Plugging $x = 9$ back into the original equation, we get $\sqrt{9 + 7} + 5 = 9$, which simplifies to $4 + 5 = 9$, a true statement. Thus, $x = 9$ is actually a solution, not a value that cannot possibly be a solution. The mistake in the reasoning is assuming $x = 9$ cannot be a solution without checking it against the original equation. The correct approach is to identify values that do not satisfy the domain of the square root function or do not satisfy the original equation upon solving. In this case, no specific values are given that cannot possibly be solutions based on the incorrect reasoning provided. The correct answer should identify values that, when plugged into the original equation, do not satisfy it, but without further calculation or incorrect assumptions, the provided choices do not accurately reflect such values based on the correct mathematical process.

Decide What Values of the Variable Cannot Possibly Be Solutions x+7+5=x\sqrt { x + 7 } + 5 = xx+7​+5=x

Decide What Values of the Variable Cannot Possibly Be Solutions $\sqrt { x + 7 } + 5 = x$