document.write( "Question 78113: Completing the square\r
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document.write( "2x² - 8x - 9 = 0 \n" );
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Algebra.Com's Answer #56020 by bucky(2189)![]() ![]() ![]() You can put this solution on YOUR website! \n" ); document.write( ". \n" ); document.write( "Don't forget, when you do a problem using the method of completing the square, you want the \n" ); document.write( "coefficient or multiplier of the \n" ); document.write( "the first thing you want to do is to divide both sides of the equation by 2. When you do \n" ); document.write( "that the problem becomes: \n" ); document.write( ". \n" ); document.write( " \n" ); document.write( ". \n" ); document.write( "Next, look at the x term. Its multiplier or coefficient is -4. Divide it by 2 and square \n" ); document.write( "the result. The division by 2 gives you -2, and squaring the -2 results in +4. \n" ); document.write( ". \n" ); document.write( "What you do next is to add +4 to the left side. But, if you add +4 then you need to \n" ); document.write( "also subtract 4 so you don't change the equation. When you do this you have: \n" ); document.write( ". \n" ); document.write( " \n" ); document.write( ". \n" ); document.write( "For the time being you don't want to mess with the \n" ); document.write( "your perfect square. But you can combine the \n" ); document.write( ". \n" ); document.write( " \n" ); document.write( ". \n" ); document.write( "Substituting this into the equation results in: \n" ); document.write( ". \n" ); document.write( " \n" ); document.write( ". \n" ); document.write( "You want to get it so only the perfect square is on the left side. So eliminate the term \n" ); document.write( " \n" ); document.write( ". \n" ); document.write( " \n" ); document.write( ". \n" ); document.write( "Now convert the left side to its equivalent square and this results in: \n" ); document.write( ". \n" ); document.write( " \n" ); document.write( ". \n" ); document.write( "Note that the -2 is the same as we got by taking half of the coefficient of the -4x in \n" ); document.write( "the original problem when we were working on creating the perfect square. \n" ); document.write( ". \n" ); document.write( "Now you can solve this for x by taking the square root of both sides. When you do that \n" ); document.write( "you get: \n" ); document.write( ". \n" ); document.write( " \n" ); document.write( ". \n" ); document.write( "Notice that the two results show that you are going to get two answers that differ \n" ); document.write( "only by the sign on the square root term ... one with a + and one with a - sign. \n" ); document.write( ". \n" ); document.write( "Finally, to solve for just x, add +2 to both sides to get: \n" ); document.write( ". \n" ); document.write( " \n" ); document.write( ". \n" ); document.write( "It is standard practice not to have a radical term in the denominator. So multiply \n" ); document.write( "the \n" ); document.write( ". \n" ); document.write( " \n" ); document.write( ". \n" ); document.write( "Substituting this results into the equation for x results in the more standard form of: \n" ); document.write( ". \n" ); document.write( " \n" ); document.write( ". \n" ); document.write( "and putting all terms over the common denominator of 2 gives you: \n" ); document.write( ". \n" ); document.write( " \n" ); document.write( ". \n" ); document.write( "and that is the form you are more likely to get by using the quadratic formula ... a \n" ); document.write( "formula that you will likely learn soon if you haven't already. \n" ); document.write( ". \n" ); document.write( "Hope these details help you to understand the process of completing the square a little more. \n" ); document.write( " \n" ); document.write( " |