Recall that completing the square required a

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Unformatted text preview: metic correctly we can guarantee that the quadratic will factor as a perfect square. Let’s do a couple of examples for just completing the square before looking at how we use this to solve quadratic equations. Example 1 Complete the square on each of the following. (a) x 2 - 16 x [Solution] (b) y 2 + 7 y [Solution] Solution (a) x 2 - 16 x Here’s the number that we’ll add to the equation. 2 2 æ -16 ö ç ÷ = ( -8 ) = 64 è2ø Notice that we kept the minus sign here even though it will always drop out after we square things. The reason for this will be apparent in a second. Let’s now complete the square. © 2007 Paul Dawkins 93 College Algebra x 2 - 16 x + 64 = ( x - 8 ) 2 Now, this is a quadratic that hopefully you can factor fairly quickly. However notice that it will always factor as x plus the blue number we computed above that is in the parenthesis (in our case that is -8). This is the reason for leaving the minus sign. It makes sure that we don...
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This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.

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