Question

Solve the following equation and re-express the answer as a complex number with the imaginary unit.  -2x^2 - 8x = -8x + 8

Answer 1

First, we start with the given equation:

\[
-2x^2 - 8x = -8x + 8
\]

Next, we can simplify the equation by moving all terms to one side. We can add \(8x\) to both sides:

\[
-2x^2 - 8x + 8x = 8
\]

This simplifies to:

\[
-2x^2 = 8
\]

Now, we can divide both sides by \(-2\):

\[
x^2 = -4
\]

Next, we take the square root of both sides. Remember, the square root of a negative number involves the imaginary unit \(i\):

\[
x = \pm \sqrt{-4} = \pm 2i
\]

Thus, the solutions to the equation are:

\[
x = 2i \quad \text{and} \quad x = -2i
\]

The final answer expressed as complex numbers with the imaginary unit is:

\[
x = 2i \quad \text{or} \quad x = -2i
\]