Algebra · Quadratic equations
Chapter 1 · 3
The idea
Completing the square
Why x² + bx is a square with a corner missing, why the bracket takes HALF of b, and how the completed form solves equations exactly and hands you the turning point for free.
A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.
In this lesson — start anywhere
Algebra · Quadratic equations
Completing the square
Why x² + bx is a square with a corner missing, why the bracket takes HALF of b, and how the completed form solves equations exactly and hands you the turning point for free.
Why it works
The bracket takes half
Expand and watch where the pieces go: . The bracket's appears doubled in the middle term. So to run this backwards for , the bracket must take half the -coefficient — and then the expansion drags in an unwanted () that has to be subtracted off:That's the whole method — halve, subtract, tidy — and expanding back verifies it every time.
Keep reading — free
The rest of the explanation, plus 2 worked examples you step through move by move.
Start freeTakes a minute — no card.