$|F_R|=\sqrt{ (16+\frac{\sqrt{2}}{2}x)^2 + (\frac{\sqrt{2}}{2}x)^2 }$
I am trying to minimize x, which is the magnitude of another vector.
Then I square both sides to simplify it
$$g(x)=|F_R|^2=16^2+16\sqrt{2}x+x^2$$
Now I need to minimize the function, so I find the critical points of the derviative of $g(x)$
$$g'(x)=0=2x+16\sqrt{2}$$
$$x=-11.3$$
The correct answer in the book is $11.3$ for the magnitude of the vector x. My answer is practically the same, except negative. Magnitudes can't be negative. What did I do wrong?