Math Hacks
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Math Hacks

How To “Complete the Square” Visually

and the Trouble with Memorization


Learning to Complete the Square

I remember learning how to “complete the square” as a teenager and I did what most students do, I memorized the steps. I was pretty good at memorization, so I got by.

But first, pick your poison!

Before we jump into the math, I’m going to give you two options 😉

Check out Math Hacks on YouTube for more video tutorials!

Quadratics: A Quick Recap

I haven’t talked about quadratics much in this series, but I really wanted to cover this topic so I’m going to assume you know quadratics are algebraic equations where the term with the highest power is 2.

Typical Instructions for Completing the Square

I could show you an example of how to complete the square by following these instructions, but honestly how much of these steps will you remember?

  • Subtract the constant to the other side.
  • Take half of the x terms coefficient, square it and add to both sides.
  • Factor the trinomial into a binomial squared.
  • Take the square root of both sides (including a plus or minus sign).
  • Finish solving for X and simplify the answer, if needed.

A Different Approach

Instead let’s use an area model to visualize how to complete the square of the following equation:



Tutorials with a fresh perspective.

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Brett Berry

Check out my YouTube channel “Math Hacks” for hands-on math tutorials and lots of math love ♥️