MHB How do I solve sqrt(5x + 3) = -2?

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The equation sqrt(5x + 3) = -2 has no solution in real numbers because the square root function is defined to yield only non-negative results. Squaring both sides leads to an incorrect statement, 2 = -2. While one might derive x = 1/5 by manipulating the equation, substituting this value back into the original equation confirms that it does not satisfy the condition. Therefore, the conclusion is that the equation has no valid solutions. The discussion emphasizes the importance of recognizing the properties of square roots in solving such equations.
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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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