Quadratic Formula Derivation

The standard form of a quadratic equation is:


Here, a,b,c, and a0

We begin by first dividing both sides by the coefficient a


We can rearrange the equation:


We can then use the method of completing the square. (Maths is Fun has a really good explanation for this technique)


On our LHS, we can clearly recognize that it is the expanded form of (x+d)2 i.e x2+2x·d+d2


Taking the square root of both sides


This gives you the world famous quadratic formula:

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