 Derive the Quadratic Formula MathBitsNotebook.com Terms of Use   Contact Person: Donna Roberts  The process of completing the square will show us how the quadratic formula was developed from solving a quadratic equation.   1. Start with a quadratic equation set = 0. 2. Move the constant to the right side. 3. Divide each term by a to get the leading coefficient to be one. 4. Get ready for a perfect square trinomial on the left side (put in the boxes). 5. To find the needed value, take half of the coefficient of the x-term, , and square it, . Add this value to both sides of the equation (put it in the boxes). 6. Square the last term on the right side. Find a common denominator on the right. 7. Combine terms on the right, placing b2 in front of -4ac in the numerator. 8. Re-write the perfect square trinomial on the left side as the square of a binomial. 9. Take the square root of both sides. Simplify the radical on the right side. 10. Subtract the constant away from x. Write as a single fraction on the right side. By completing the square, we discovered the quadratic formula!!  