How to Remember the Rules for Solving Quadratic Equations

Let’s be honest, the moment someone says “quadratic equations,” most students either sigh, look away, or feel that mini panic rise in their chest. You’re not alone. We’ve all been there. Whether you’re revising for GCSEs or just trying to get through your maths homework without throwing your calculator, this blog is for you. Let’s break it down together, no scary words, no confusing steps. Just real talk and smart tips that actually help.

First: What Even Is a Quadratic Equation?

A quadratic equation looks like this:

ax² + bx + c = 0

Where:

• a, b, and c are just numbers (they can be positive, negative, or zero),

• x is the variable (the thing you’re solving for), and

• It always has x² in it (that’s what makes it “quadratic”).

Your goal? Find out what x equals.

Okay… But Why Is It So Hard to Remember the Rules?

Because it feels like there’s a lot to remember:

• The quadratic formula (hello, tongue twister!),

• Factorising (which only works sometimes),

• Completing the square (cue the headache),

• And remembering when to use what.

  
  

But here’s the secret: you don’t have to remember everything at once. You just need to know which method to use when, and have a few memory tricks in your pocket.

Let’s take this step-by-step.

1. When in Doubt, Try to Factorise First

Factorising is your best friend — when it works. It’s the easiest and fastest way to solve a quadratic.

Here’s how you know it might work:

• The equation looks like x² + 5x + 6 = 0

• You can find two numbers that multiply to the last number (c) and add up to the middle number (b)

In our example:6 = 2 × 3 and 2 + 3 = 5 — perfect!

So we rewrite it as:

(x + 2)(x + 3) = 0Then solve:x = -2 or x = -3

Memory tip: If the numbers are small and neat, factorising is worth trying first. If the numbers are big, weird, or include decimals, skip them!

2. If You Can’t Factor It, Use the Quadratic Formula

You know it. You’ve seen it. It goes:

x = [-b ± √(b² - 4ac)] / 2a

It looks scary, but it always works. Think of it as your “emergency tool”, the one that gets the job done, even if it’s messy.

How to remember the formula:

Make it a song. No joke. Tons of students remember it by singing:

“x equals minus b, plus or minus square root, b squared minus four a c, all over two a” 

funny? Yes.Effective? Also yes.

Memory tip: This formula is always safe to use; it works when factorising doesn’t.

3. Completing the Square: The Last Resort (but it’s useful too)

You might only use this when your teacher or exam question tells you to, but it’s a clever method.

It helps you:

• Solve quadratics that can’t be factorised

• Rewrite a quadratic in a different form (which helps in graphs and transformations)

  
  

Honestly? You don't need to use this one every day, but it’s good to understand the idea behind it.

Memory tip: This method works well when the coefficient of x² is 1 (like in x² + 6x + 8). The idea is to create a perfect square, like turning x² + 6x into (x + 3)²

4. Quick Guide: How to Choose the Right Method

Your Equation Looks Like	Try This Method
Nice whole numbers, easy to factor	Factorising
Weird numbers or no clear factors	Quadratic Formula
Asked to complete the square	Complete the Square
Want to sketch a graph	Completing the Square

5. Extra Tips for Remembering the Rules

• Write them out, daily, repetition makes it stick.

• Make a cheat sheet for yourself, just one page, with a sample of each method.

• Practice with colour-coding, highlight steps in different colours so your brain connects better.

• Teach a friend, if you can explain it, you actually know it!

Finally

Quadratic equations are not your enemy. They're just puzzles — and once you know which method to use, and when, it becomes a lot less stressful. You don’t need to be a maths genius to remember the rules. You just need the right tools, a few shortcuts, and a bit of practice. And if you’re preparing for your GCSEs and still feeling unsure, you don’t have to do it alone.

At i-eSchool, we offer conventional academic lessons and expert preparatory support for GCSE, A-level and 11+, tailored to your child’s pace, with teachers who know how to make even the scariest maths topics feel manageable. So breathe, shake off the stress, and give those quadratics another try. You’ve got this!