Derive the Quadratic Formula
The quadratic formula is perhaps the most famous equation of algebra. Completing the square to derive this formula combines all five equation manipulation functions.
Multiply both sides by 
.
Add 
to both sides.
Factor the left-hand side.
Take the positive square root of both sides.
Cancel the square root of the square.
Subtract 
from both sides.
Divide both sides by 
to obtain the quadratic formula for 
with positive square root.
