Question

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Complex Numbers Unit Test
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Question
Solve the equation −x2−3x=5−3x
and re-express the answer as a complex number with the imaginary unit.(1 point)
±

Answer 1

To solve the equation \(-x^2 - 3x = 5 - 3x\), we first simplify it:

1. Move all terms to one side:
\(-x^2 - 3x - 5 + 3x = 0\)
\(-x^2 - 5 = 0\)

2. Rearrange:
\(-x^2 = 5\)

3. Divide by -1:
\(x^2 = -5\)

4. Take the square root:
\(x = \pm \sqrt{-5}\)

5. Express using the imaginary unit \(i\):
\(x = \pm i \sqrt{5}\)

Thus, the answer is:

\(\pm i \sqrt{5}\)