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

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SUMMARY

The equation sqrt(5x + 3) = -2 has no solutions in the realm of real numbers. Squaring both sides leads to the incorrect statement 2 = -2, indicating a fundamental issue with the original equation. The square root function, defined to return only non-negative values, confirms that sqrt(5x + 3) cannot equal a negative number. Therefore, the conclusion is that this equation does not yield any valid solutions.

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

littapple said:
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.
 
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.
 

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