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Lesson 118

Lesson 118. LESSON PRESENTATION. Example 118.1. Example 118.3. Example 118.2. Completing the Square. Completing the Square.

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Lesson 118

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  1. Lesson 118 LESSON PRESENTATION Example 118.1 Example 118.3 Example 118.2 Completing the Square

  2. Completing the Square We have been solving quadratic equations of the type: ax2 + bx + c = 0. In the equations like this that we have solved so far, the trinomial factored and we used the zero-product property to solve for x. When the quadratic does not factor, we cannot use factoring and the zero-product property to solve. So…we must find another method. This method has already been developed for you and is called “completing the square”. Let’s first consider the background for the “completing the square “ method. Remember the Difference of Two Squares Theorem If p and q are real numbers and if p 2 = q 2, then p = q or p = -q Or we could write,

  3. Completing the Square Consider the following equation: As a matter of fact, any quadratic equation can be written in such a way that we have two squares equal to each other. Or…. The process of writing an equation in this form is called “completing the square”.

  4. Completing the Square Example 118.1 Solveby completing the square. We first rewrite the equation in descending powers of the variable on the left-hand side of the equals sign with zero on the right side. Next, we move the constant term to the right side of the equation using the additive property. We must now determine the constant that we need to use to make the left side a perfect square trinomial.

  5. Completing the Square Example 118.2 Solveby completing the square. We first rewrite the equation in descending powers of the variable on the left-hand side of the equals sign with zero on the right side. Next, we move the constant term to the right side of the equation using the additive property. We must now determine the constant that we need to use to make the left side a perfect square trinomial.

  6. Completing the Square Example 118.3 Solveby completing the square.

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