On this website I previously showed you **why the formulas used to complete the square work** – and how they can be used to **derive formulas such as the quadratic equation.** Now, I’ll be doing something different, but related… On this post, I’ll be showing you **how to come up with the formulas (2 in total) used to complete the square – geometrically**.

**Completing the Square Formula (Derivation 1):**

In the diagram above, what we can see is that:

This means that:

**Completing the Square Formula (Derivation 2):**

In the diagram above, what we can see is that:

This means that:

I hope these **geometrical proofs** have helped you better understand why the formulas we use to complete the square are in existence. Thanks for reading! ðŸ˜€