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In this section, we will work on completing the square. It's a lot of information, so you might want to go back a read a few sections. We have been using the quadratic equation quite often so far to solve problems, and there are many ways to solve it. We have been doing them by factoring and graphing. In this section, we will focus on completing the square method of solving it. This method is only sometimes more efficient than the other methods, but here we will learn it. To do completing the square, follow these steps:At first, you will need to isolate the variable on one side of the equation. Then, you will need to factor out a perfect square somewhere on that side. Then, complete the square by adding or subtracting to complete the perfect square. Finally, solve for your variable. What is nice about completing the square is that you can solve for "x", "y", or "z". Here are some examples: Example 1: a. The equation is = −4. First, isolate the variable on one side of the equation. Then factor out a perfect square somewhere on that side of the equation. Then complete the square by adding or subtracting to complete the perfect square. The perfect square that you factor out is 2 × 2 = 4, so you have to add or subtract 4 to complete it to be a true perfect square. The completed perfect square looks like this: = 16 − 4 = 12 + 4 = 16, so your answer is . b. Next, simplify the right side of the equation by dividing both sides by 16 and writing it in factored form. You get: (x + 4) (x − 4) = 0. Now solve the equation. To solve this, we use the quadratic formula: = [±(√ [((x + 4)(x − 4))]/16]. To find the value of x when this expression equals zero, we substitute (x + 4) and (x − 4) for "a" and "b" in the quadratic formula: = [±((√ [((x + 4)(x − 4))]/16] = [-(4√ [(4 × 8)/16]/2])/2]. To find the value of x when this expression equals zero, we substitute (x + 4) and (x − 4) for "a" and "b" in the quadratic formula: = [±((−4)/2])/2] = [±(−2)/2). To find the value of x when this expression equals zero, we substitute (x + 4) and (x − 4) for "a" and "b" in the quadratic formula: = [-(4√ [(4 × 8)/16]/2])/2]. cfa1e77820