1. **State the problem:** Solve the equation $x^2 + y^2 + z^2 = 14$ using the Gaussian method. 2. **Understand the problem:** The equation $x^2 + y^2 + z^2 = 14$ represents a sphere in three-dimensional space, not a system of linear equations. The Gaussian method (Gaussian elimination) is used to solve systems of linear equations, not quadratic equations. 3. **Important note:** Since this is a single quadratic equation with three variables, it does not have a unique solution but rather an infinite set of solutions forming a sphere. 4. **Gaussian method applicability:** Gaussian elimination applies to linear systems of the form $Ax = b$. Here, the equation is nonlinear, so Gaussian elimination is not applicable. 5. **Conclusion:** The equation $x^2 + y^2 + z^2 = 14$ cannot be solved using the Gaussian method. Instead, it describes all points $(x,y,z)$ on the surface of a sphere with radius $\sqrt{14}$. **Final answer:** The set of solutions is all points satisfying $$x^2 + y^2 + z^2 = 14,$$ which is a sphere of radius $\sqrt{14}$ centered at the origin.