Question

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)
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Answer 1

To solve the equation \(-x^2 - 3x = 5 - 3x\), we can start by simplifying it.

First, let's move all terms to one side so that we have zero on one side:

\[
-x^2 - 3x - 5 + 3x = 0
\]

This simplifies to:

\[
-x^2 - 5 = 0
\]

Next, we can multiply through by -1 to make it easier to work with:

\[
x^2 + 5 = 0
\]

Now, we subtract 5 from both sides:

\[
x^2 = -5
\]

To find \(x\), we take the square root of both sides:

\[
x = \pm \sqrt{-5}
\]

Using the imaginary unit \(i\), where \(i = \sqrt{-1}\), we can express the solutions as:

\[
x = \pm \sqrt{5}i
\]

Thus, the solutions to the equation \(-x^2 - 3x = 5 - 3x\) expressed as complex numbers are:

\[
x = \sqrt{5}i \quad \text{and} \quad x = -\sqrt{5}i
\]