Solving x and Saving the World: Algebraic Techniques in Real Life

Algebraic techniques might feel like a collection of classroom drills—substitution, factorisation, completing the square—but these methods are actually the backstage crew to much of our modern tech. Whether you’re unlocking your phone, mapping a route or playing a video game, you’re calling on the same algebraic tricks you first met in Stage 5. In this post, we’ll pull back the curtain on how these simple tools make a big impact in the real world.

Where did this come from?

Around 825 AD, the Persian mathematician al-Khwarizmi wrote a groundbreaking book called Hisab al-jabr w’al-muqabala (“the calculation of restoration and balancing”). In it, he showed how to turn messy quadratic problems into neat squares—the very idea behind “completing the square.” Fast forward to the 16th century and François Viète began using letters for unknowns and coefficients, giving birth to the symbolic algebra we know today.

Where you'll see this in real life

1. GPS Triangulation: Your phone figures out your location by solving systems of simultaneous equations—think two or three circles intersecting to pinpoint you on the map. 2. Cryptography: The security behind RSA encryption relies on factorisation (breaking a big number into smaller primes). It’s the same idea you learn when you factorise polynomials, just on a much grander scale. 3. Video Game Physics: Calculating where a projectile will land uses quadratic equations. By completing the square, game engines find the highest point of a jump or the perfect arch of a thrown object. 4. Chemical Equation Balancing: Chemists balance reactions by setting up linear equations for each element and using substitution or elimination to find the right coefficients.

A common misconception

A lot of students think algebraic techniques are just abstract puzzles with no use beyond the classroom. In reality, mastering the why behind substitution, factorisation and completing the square trains you to recognise patterns, simplify complex problems and build the logic that powers everything from smartphones to spacecraft.