# Is there an easy way of remembering the quadratic formula?

##### 2 Answers

Quick writing

#### Explanation:

Here's someone else's mnemonic:

From square of b, take 4ac;

Square root extract, and b subtract;

Divide by 2a; you’ve x, hooray!

Here's what I think is the best way...

#### Explanation:

The very best way to remember it is to learn how to derive it.

We will complete the square and use the difference of squares identity:

#A^2-B^2=(A-B)(A+B)#

with

Given:

#ax^2+bx+c = 0" "# with# \ a != 0#

Multiply by

#0 = 4a^2x^2+4abx+4ac#

#color(white)(0) = (2ax)^2+2b(2ax)+4ac#

#color(white)(0) = (2ax)^2+2b(2ax)+b^2+4ac-b^2#

#color(white)(0) = (2ax+b)^2-(b^2-4ac)#

#color(white)(0) = (2ax+b)^2-(sqrt(b^2-4ac))^2#

#color(white)(0) = ((2ax+b)-sqrt(b^2-4ac))((2ax+b)+sqrt(b^2-4ac))#

#color(white)(0) = (2ax+b-sqrt(b^2-4ac))(2ax+b+sqrt(b^2-4ac))#

Hence:

#2ax = -b+-sqrt(b^2-4ac)#

Then dividing both sides by

#x = (-b+-sqrt(b^2-4ac))/(2a)#