# How do I solve sqrt(5x + 3) = -2?

#### littapple

##### New member
What's the answer to the problem sqrt(5x+3)=-2, solving for x?
If you square both sides, you get 2=-2, which is wrong. Does it have to
do with complex/imaginary numbers? Or does it have no answer at all?

#### eddybob123

##### Active member
Re: What is sqrt(5x+3)=-2? Help me solve?

What's the answer to the problem sqrt(5x+3)=-2, solving for x?
If you square both sides, you get 2=-2, which is wrong. Does it have to
do with complex/imaginary numbers? Or does it have no answer at all?
If you square both sides you get
$$5x+3=4$$
And following that gives
$$5x=1$$
$$x=\frac{1}{5}$$
However, when putting in the value of x into your original equation, we want to take only the positive root, so your equation has no solutions.

#### HallsofIvy

##### Well-known member
MHB Math Helper
Re: What is sqrt(5x+3)=-2? Help me solve?

When working with real numbers, $$\sqrt{a}$$ is, by definition, the positive number whose square is a. You should have been able to see, immediately, that $$\sqrt{5x+3}= -2$$ has NO solution.