Completing the square is a method that helps us solve quadratic equations. Here’s how to do it step-by-step:

1. Standard Form: Start by writing the quadratic equation in this form:
   $ax^2 + bx + c$

2. Factor out 'a': If 'a' is not 1, take 'a' out from the first two parts:
   $a(x^2 + \frac{b}{a}x) + c$

3. Add and Subtract: Next, take half of the number in front of 'x' (the coefficient), square it, and then add and subtract it inside the parentheses:
   $a\left(x^2 + \frac{b}{a}x + \left(\frac{b}{2a}\right)^2 - \left(\frac{b}{2a}\right)^2\right) + c$

4. Rewrite: Now, we rewrite this as:
   $a\left(\left(x + \frac{b}{2a}\right)^2 - \left(\frac{b}{2a}\right)^2\right) + c$

5. Simplify: Finally, we can make it simpler to get to:
   $a\left(x + \frac{b}{2a}\right)^2 + \left(c - \frac{b^2}{4a}\right)$

And that's how you complete the square! This process helps make quadratic equations easier to work with.