Answer:


Explanation:
In order to solve the quadratic equation:
for Q.
we can use a substitution to simplify the equation.
Let's define:

So, the equation becomes:

This is a quadratic equation in terms of x.
To solve for x, we can use the quadratic formula:

In this case, the coefficients are a = 1, b = -2, and c = -3.
Substituting these values into the quadratic formula:




So, we have two possible solutions for x.


Now, we'll use the relationship
to find the corresponding values of Q.
For
:





For
:





Keep in mind that the arctangent function has multiple angles that satisfy its equation.
So, the solutions for Q can also be represented as:

and

where K is an integer allowing for multiple solutions due to the periodic nature of the tangent function.