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.