Completing the Square

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In this section, we continue to learn how to solve quadratic equations without factoring. Here, we will learn a general method known as solving quadratic equations by completing the square. Using this method, we can solve any quadratic equation whether it can be factored or not. To use this method, we begin by writing the left side of the equation as a perfect square trinomial. If this does not exist already, we follow the steps to create one:
  • Make sure the squared term has a coefficient of 1
  • Place all variable terms on one side and all constants on the other
  • Complete the square by taking one-half of the first-degree term and squaring it - add this amount to both sides of the equation
  • Factor the left side and solve the equation using the square root property
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