document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=141840>Question 141840</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi I need help in understanding one of the steps in \"completing the square\" for a quadratic equation.Here is my problem\r<BR>\n" );
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document.write( "x^2+9x+8=0\r<BR>\n" );
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document.write( "IN the 2ND step my homework tells me that I have to multiply the equation by A, whatever value it has.Now everytime they show a model there is a different value for \"A\" everytime.How do I find the value of \"A\" for my own homework equations.Here is one of my models from my school...\r<BR>\n" );
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document.write( "Solve x^2 + 7x + 12 = 0 by completing the square.\r<BR>\n" );
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document.write( "1. Write the quadratic equation in general for and identify A and B.\r<BR>\n" );
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document.write( "A is 1 and B is 7.\r<BR>\n" );
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document.write( "2. Multiply the terms of the equation by 4A.<BR>\n" );
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document.write( "4A is 4:  4[x^2 + 7x + 12]= 4[0]<BR>\n" );
document.write( "4x^2 + 28x + 48 = 0\r<BR>\n" );
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document.write( "3.Isolate the constant term on the right side of the equation.\r<BR>\n" );
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document.write( "4x^2 + 28x = -48\r<BR>\n" );
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document.write( "4.Add B^2 to each side of the equation.\r<BR>\n" );
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document.write( "B^2 is 49: [4x^2 + 28x] +49 = [-48]+49<BR>\n" );
document.write( "4x^2 + 28x + 49 = 1\r<BR>\n" );
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document.write( "5.Factor the left side of the equation to the square of a binomial.\r<BR>\n" );
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document.write( "(2x + 7)(2x + 7) = 1<BR>\n" );
document.write( "(2x + 7)^2 = 1\r<BR>\n" );
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document.write( "   Now solve:<BR>\n" );
document.write( "               1^2 is 1, so             (-1)^2 is 1, so<BR>\n" );
document.write( "               2x + 7 = 1                2x + 7 = -1<BR>\n" );
document.write( "               2x = -6                   2x = -8<BR>\n" );
document.write( "               x = -3                    x = -4  \r<BR>\n" );
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document.write( "The solution set is {-4, -3}.\r<BR>\n" );
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document.write( "What I dont understand is step 2 how did they decide to multiply the equation by 4? Why dont they use any other number like 2 or 6?\r<BR>\n" );
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document.write( "I hope I gave you enough information.Thanks for your help... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #103312 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=103312\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Well, the obvious answer is that 4 is a perfect square, while 2 and 6 are not.  Having said that, the process you showed is not the one that I use.\r<BR>\n" );
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document.write( "Here's my process given <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Move the constant term to the right:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx=-c ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx=-c\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide both sides by the lead coefficient (if it is already 1, you don't have to do anything)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%28b%2Fa%29x=%28%28-c%29%2Fa%29 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28b%2Fa%29x=%28%28-c%29%2Fa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide the coefficient on the 1st degree term by 2, and then square the result.  Add that result to both sides of the equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%28b%2Fa%29x%2B%28b%5E2%2F4a%5E2%29=%28b%5E2%2F4a%5E2%29%2B%28%28-c%29%2Fa%29 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28b%2Fa%29x%2B%28b%5E2%2F4a%5E2%29=%28b%5E2%2F4a%5E2%29%2B%28%28-c%29%2Fa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Factor the left now that it is a perfect square.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B%28b%2F2a%29%29%5E2=%28b%5E2%2F4a%5E2%29%2B%28%28-c%29%2Fa%29 ALIGN=MIDDLE  ALT=\"%28x%2B%28b%2F2a%29%29%5E2=%28b%5E2%2F4a%5E2%29%2B%28%28-c%29%2Fa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Take the square root of both sides.<BR>\n" );
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document.write( "Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%2F2a ALIGN=MIDDLE  ALT=\"-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-b%2F2a%2B-sqrt%28%28b%5E2%2F4a%5E2%29%2B%28%28-c%29%2Fa%29%29 ALIGN=MIDDLE  ALT=\"x=-b%2F2a%2B-sqrt%28%28b%5E2%2F4a%5E2%29%2B%28%28-c%29%2Fa%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplify.<BR>\n" );
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document.write( "Hope that helps.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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