Rule for Completing the Square
Date: 03/15/2002 at 12:08:28 From: Irina Subject: Square equation Which of the following expressions should be placed in each set of parentheses below in order to solve the equation by completing the square? x^2+6x+(?)=15+(?) A.3/2 B.3 C.6 D.9 I have no clue to answer this question. Thanks.
Date: 03/15/2002 at 14:52:03 From: Doctor Rick Subject: Re: Square equation Hi, Irina. The idea is that you have the equation x^2 + 6x = 15 and you want to solve it by the method of completing the square. This means that you want to make the left side into the square of a binomial, which you can do by adding the correct constant to it; and of course, to keep the equation equivalent to the original, you must add the same constant to the right side as well. How do you tell what constant to add? We want to end up with something like (x + C)^2 Expand this: x^2 + 2Cx + C^2 Compare with what you have: x^2 + 6x + ___ The coefficient of x, 2C, should be equal to 6: 2C = 6 C = 6/2 = 3 Then what goes in the blank? It's C^2, and since C = 3, it's 3^2 = 9 that goes in the blank. x^2 + 6x + (9) = 15 + (9) Then we can solve the problem: (x + 3)^2 = 24 x + 3 = sqrt(24) or -sqrt(24) x = -3+sqrt(24) or -3-sqrt(24) You can simplify the square root of 24, but that's another topic. Now that we've worked one problem out in detail, we can see a simple rule for completing the square - at least if the coefficient of x^2 is 1, as in this example. Just take half the coefficient of x, and square it. (6/2)^2 = 9 If you have any problems in which the coefficient of x is not 1, then work it out in the same way I did this example, and see if you can find the rule for this more general case. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/
Date: 03/18/2002 at 11:07:11 From: Irina Subject: Square equation Thanks a lot; that information was very helpful. Irina
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