The isolated solution for k is given by (F^2 / P^2) - 8.
The equation is:
F = P√(8 + k)
We need to isolate k in order to solve for it. Here are the steps involved:
Square both sides of the equation to get rid of the square root. This will give us a quadratic equation.
F^2 = P^2 * (8 + k)
Expand the right side of the equation.
F^2 = 8P^2 + kP^2
Move the k term to one side of the equation.
kP^2 = F^2 - 8P^2
Divide both sides by P^2 to isolate k.
k = (F^2 - 8P^2) / P^2
Therefore, the solution for k is:
k = (F^2 - 8P^2) / P^2
Square both sides: F^2 = P^2 * (8 + k)
Expand: F^2 = 8P^2 + kP^2
Move the k term: kP^2 = F^2 - 8P^2
Isolate k: k = (F^2 - 8P^2) / P^2
In the final expression, k is isolated. To simplify it further, you can factor out P^2 from the numerator:
k = (F^2 - 8P^2) / P^2 = F^2 / P^2 - 8
So, the solution for k is F^2 / P^2 - 8.