Final answer:
The question involves solving an equation with a square root and a variable. Squaring both sides of \(\sqrt{x + 2} = -x\) leads to a quadratic equation, which can be solved using the quadratic formula. It is important to check for extraneous solutions.
Step-by-step explanation:
The student is asking about how to find the set of solutions to a given equation that involves a square root and a variable x. The correct interpretation of the provided equation is \(\sqrt{x + 2} = -x\). In some cases like this one, the equation may result in two solutions because we are dealing with a variable that is squared at some point. To solve this equation, we need to isolate the variable and sometimes use the quadratic formula.
First, we should square both sides of the equation to eliminate the square root, which gives us \(x + 2 = x^2\). Next, we rearrange the equation into the standard quadratic form \(x^2 - x - 2 = 0\), and then we can use the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\) to find the values of x.