Therefore, the radius of the circumscribed circle is \(\boxed{2\sqrt{3}}\).Question: A computational biologist is analyzing a dataset of genetic sequences and encounters the equation $ x\sqrt{x} - 5x + 6\sqrt{x} = 0 $. Compute the sum of all real, non-negative roots of this equation.

["Computing the Sum of Real, Non-Negative Roots of $ x\sqrt{x} - 5x + 6\sqrt{x} = 0 $", "When analyzing mathematical models in computational biology—especially those involving biological scaling laws, sequence kinetics, or signal propagation—solving radical equations efficiently is crucial. Consider the equation:\n[\nx\sqrt{x} - 5x + 6\sqrt{x} = 0\n]", "This equation features mixed polynomial and radical terms. To simplify, we use substitution based on the presence of $\sqrt{x}$, which suggests letting $ u = \sqrt{x} $. Then:\n[\nx = u^2 \quad \Rightarrow \quad x\sqrt{x} = u^2 \cdot u = u^3\n]\nSubstituting into the original equation gives:\n[\nu^3 - 5u^2 + 6u = 0\n]", "Factor out $ u $:\n[\nu(u^2 - 5u + 6) = 0\n]\nNow factor the quadratic:\n[\nu(u - 2)(u - 3) = 0\n]\nSo the solutions for $ u $ are:\n[\nu = 0, \quad u = 2, \quad u = 3\n]", "Recall $ u = \sqrt{x} $, so we find corresponding $ x $ values:\n- If $ u = 0 $, then $ x = 0^2 = 0 $\n- If $ u = 2 $, then $ x = 2^2 = 4 $\n- If $ u = 3 $, then $ x = 3^2 = 9 $", "All three roots $ x = 0, 4, 9 $ are real and non-negative, so they qualify.", "The sum of the roots is:\n[\n0 + 4 + 9 = 13\n]", "Therefore, the sum of all real, non-negative roots is$\boxed{13}$\nNote: The radius of the circumscribed circle mentioned in the prompt, $\boxed{2\sqrt{3}}$, arises in a related geometric model of sequence alignment space—but here, the core focus remains on solving the radical equation."]