Derive the quadratic formula (Hint: complete the square)

Firstly, the quadratic formula finds the roots of a quadratic equation. 
So this means f(x) = 0. A general polynomial with highest power 2 looks like: ax² + bx +c.
Usings the two facts we just stated, we solve for the roots of ax² + bx +c = 0. ax² + bx +c = 0
x² + (b/a)x + (c/a) = 0
USINGING THE HINT
(x + (b/2a))² - (b/2a)² + (c/a) = 0
(x + (b/2a))² = (b/2a)² -(c/a)  
Make the right hand side all one fraction
(x + (b/2a))² = (b²/4a²) - (4ac/4a²)
(x + (b/2a))² = (b²-4ac) / 4a²
Squareroot both sides
x + (b/2a) = (+/-) (b²-4ac)^1/2 / 2a          (The (+/-) comes from the squareroot having 2 sol's. e.g 4^1/2 = 2 or -2)
x = (-b (+/-) (b²-4ac)^1/2) / 2a