document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=389646>Question 389646</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solveby factoring when first coefficient is a negative number.  please take me thru each step:\r<BR>\n" );
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document.write( "-2x^2 + 13x - 21\r<BR>\n" );
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document.write( "they say the answer is 3, 7/2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #276159 by </B><A HREF=/tutors/aboutme.mpl?userid=texttutoring><B>texttutoring(324)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=texttutoring><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=texttutoring><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=276159\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Recall the general form for a quadratic equation: \r<BR>\n" );
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document.write( "ax^2 + bx + c\r<BR>\n" );
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document.write( "-2x^2 + 13x - 21\r<BR>\n" );
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document.write( "We will use the Decomposition Method for factoring.\r<BR>\n" );
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document.write( "First, multiply a*c = (-2)(-21) = 42\r<BR>\n" );
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document.write( "So you need to find two numbers that multiply to 42 and add up to the b term, +13. This is pretty easy: the numbers are 7 and 6.\r<BR>\n" );
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document.write( "Now the hard part is to decompose the b term, +13, into these two factors. Notice that I list 6x first, so that it pairs with the 2x^2, and the 7x second, so that it pairs with the 21 at the end. \r<BR>\n" );
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document.write( "-2x^2 + 13x - 21<BR>\n" );
document.write( "-2x^2 + 6x + 7x - 21\r<BR>\n" );
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document.write( "Next, factor out the -2x and 7 from each. Note that you are left with identical terms, (x-3) for each.\r<BR>\n" );
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document.write( "-2x(x-3) + 7(x-3)\r<BR>\n" );
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document.write( "Combine the -2x and 7 into one bracket:\r<BR>\n" );
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document.write( "(-2x + 7)(x-3)\r<BR>\n" );
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document.write( "This leaves you with two answers, which you can find by setting each bracket to zero, and solving for x:\r<BR>\n" );
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document.write( "-2x+7 =0<BR>\n" );
document.write( "7=2x<BR>\n" );
document.write( "x=7/2\r<BR>\n" );
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document.write( "x-3=0<BR>\n" );
document.write( "x=3\r<BR>\n" );
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document.write( "Hope this helps! Let me know if you're confused by anything.  </SPAN>\n" );
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