Chapter 3 - Quadratic Functions - 3.2 The Vertex of a Parabola - Exercises and Problems for Section 3.2 - Skill Refresher - Page 127: S3

$(c+\frac{3}{2})^2-\frac{37}{4}$

Since $(c+\frac{3}{2})^2=c^2+\frac{3}{2}c+\frac{3}{2}c+\frac{3^2}{2^2}=c^2+3c+\frac{9}{4}$, $c^2+3c-7$ can be written as $$(c+\frac{3}{2})-\frac{9}{4}-7=(c+\frac{3}{2})^2-\frac{9}{4}-\frac{28}{4}=(c+\frac{3}{2})^2-\frac{37}{4}$$