The Quadratic Formula used to solve equations of the form . It is: * Proof: Dividing our quadratic equation by (which is allowed because is non-zero), we have which is equivalent to The equation is now in a form in which we can conveniently complete the square. To "complete the square" is to add a constant (i.e., in this case, a quantity that does not depend on ) to the expression to the left of "", that will make it a perfect square trinomial of the form . Since in this case is , we must have , so we add the square of to both sides, getting Taking square roots of both sides yields