Solve the equation −x2−3x=5−3x

Question

and re-express the answer as a complex number with the imaginary unit.
explain how you get the answer and the answer is √5

Answer 1

To solve the equation −x^2−3x=5−3x, we can start by simplifying both sides. We notice that both sides have a −3x term, so we can subtract it from both sides to simplify the equation:

−x^2 − 3x + 3x = 5 − 3x + 3x

Simplifying further:

−x^2 = 5

Now, we want to solve for x. To do this, we'll isolate x^2 by multiplying both sides of the equation by -1:

x^2 = -5

Finally, to find x, we take the square root of both sides:

√(x^2) = √(-5)

Since we want to express the answer as a complex number, we know that the square root of a negative number is an imaginary number. Therefore, we can express the answer as:

x = ±√5 i

So, the solution to the equation −x^2−3x=5−3x as a complex number is ±√5 i.