1. **State the problem:** Complete the square for a quadratic expression, typically in the form $ax^2 + bx + c$. 2. **Formula and rules:** To complete the square for $x^2 + bx + c$, rewrite it as $\left(x + \frac{b}{2}\right)^2 - \left(\frac{b}{2}\right)^2 + c$. 3. **Example:** Suppose we complete the square for $x^2 + 6x + 5$. 4. **Step-by-step:** - Identify $b = 6$. - Calculate $\frac{b}{2} = \frac{6}{2} = 3$. - Square it: $3^2 = 9$. - Rewrite the expression: $$x^2 + 6x + 5 = \left(x + 3\right)^2 - 9 + 5$$ - Simplify constants: $$\left(x + 3\right)^2 - 4$$ 5. **Final answer:** The completed square form is $$\boxed{\left(x + 3\right)^2 - 4}$$. This method helps to easily find the vertex of a parabola or solve quadratic equations.