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The Quadratic Formula used to solve equations of the form . It is:
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
The left side is now a perfect square; it is the square of . The right side can be written as a single fraction; the common denominator is . We get
Taking square roots of both sides yields
Subtracting from both sides, we get