What is the set of all solutions to the equation square root of (x+2)=-x

D)There are no solutions to the given equation

Show your work, or tell me how you got your answer thanks.

I can show you the algebra, but first I want to draw your attention to the answer choices. Look at them! They’re beautiful. They show you that if you just try –1 and 2—just two numbers—you’ll know what’s right.

So, try –1:


Yep, that works!

Now, try 2:


Nope, that does NOT work. When you have the square root function, you only return positive numbers.

So the answer is B.

Now, the algebra. You have to start by squaring both sides.


That tells you that the set of possible solutions is \left\{2,-1\right\}. Note that the answer choices already told you that!

But remember: we squared both sides of the equation when we started, which means we could have introduced extraneous solutions. So now you have to go back and check 2 and –1 in the original equation, just like I already did above.

Long story short, next time you see a problem like this, just jump right into checking the numbers from the answer choices. Even if you do the long-way algebra, you’re going to end up needing to.

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