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Find the solution set of the equation 𝑥 squared plus three equals zero in the real numbers.
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Let’s begin by finding the solution.
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So we need to solve for 𝑥.
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So let’s go ahead and subtract three from both sides of the equation.
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So we have that 𝑥 squared is equal to negative three.
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Now, to solve for 𝑥, we need to square root both sides of the equation.
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So 𝑥 is equal to the square root of negative three.
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But we want the solution set of the equation that’s in the real numbers.
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And the square root of a negative number is not in the real numbers.
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It’s in the imaginary numbers.
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So there are no real solutions in this set.
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Therefore, the solution set is empty, which is called the empty set or the null set.