# Quadratic Equations: Completing the Square First recall the algebraic identities We shall use these identities to carry out the process called Completing the Square. For example, consider the quadratic function What can be added to yield a perfect square? Using the previous identities, we see that if we put 2e=8, that is e=4, it is enough to add to generate a perfect square. Indeed we have It is not hard to generalize this to any quadratic function of the form . In this case, we have 2e=b which yields e=b/2. Hence Example: Use Complete the Square Method to solve Solution.First note that the previous ideas were developed for quadratic functions with no coefficient in front of . Therefore, let divide the equation by 2, to get which equivalent to In order to generate a perfect square we add to both sides of the equation Easy algebraic calculations give  which give the solutions to the equation We have developed a step-by-step procedure for solving a quadratic equation; or, in other words, an algorithm for solving a quadratic equation. This algorithm can be stated as a formula called Quadratic Formula. [Algebra] [Complex Variables]
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