Beginning Algebra
When coefficients are very large and floating-point approximations are required, completing the square does not necessarily avoid arithmetic and may not be the best numerical method
When the discriminant is negative and you do not want complex numbers to appear in your solution, completing the square will still produce complex results, just as the quadratic formula does
When integer factors exist and you only need numerical roots quickly, factoring is usually faster and simpler than completing the square
When you need the vertex form to graph the parabola or to determine the maximum or minimum values, and you want an exact algebraic expression for the vertex, completing the square will directly provide this information