document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=171271>Question 171271</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This came from a Factoring Polynomials Sections..\r<BR>\n" );
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document.write( "I need help finding all the solutions to \r<BR>\n" );
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document.write( "-17w=8w^2+5w-40 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #126443 by </B><A HREF=/tutors/aboutme.mpl?userid=midwood_trail><B>midwood_trail(310)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=midwood_trail><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=126443\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I Will set up the quadratic equation and allow you to factor.<BR>\n" );
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document.write( "-17w = 8w^2 + 5w - 40\r<BR>\n" );
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document.write( "Adding 17w to both sides and setting up equation to equal zero, I get this:\r<BR>\n" );
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document.write( "8w^2 + 5w + 17w - 40 = 0\r<BR>\n" );
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document.write( "We now combine like terms and get:\r<BR>\n" );
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document.write( "8w^2 + 22w - 40 = 0\r<BR>\n" );
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document.write( "To reduce those big numbers on the left side of the equation, I'll divide each number by 2.\r<BR>\n" );
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document.write( "After doing so, I get this:\r<BR>\n" );
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document.write( "4w^2 + 11w - 20 = 0\r<BR>\n" );
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document.write( "Can you take it from here?\r<BR>\n" );
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document.write( "If not, write back.\r<BR>\n" );
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document.write( "I received your reply.\r<BR>\n" );
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document.write( "You asked:\r<BR>\n" );
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document.write( "Is the answer -4w?\r<BR>\n" );
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document.write( "Think about it for a minute.\r<BR>\n" );
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document.write( "Have you solved for w?\r<BR>\n" );
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document.write( "To solve for a letter means that the letter must equal an answer.\r<BR>\n" );
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document.write( "In other words, w should equal some value.\r<BR>\n" );
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document.write( "Here is your quadratic equation as I reduced it in my first reply:\r<BR>\n" );
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document.write( "4w^2 + 11w - 20 = 0\r<BR>\n" );
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document.write( "We multiply 4 times -20 and get -80.\r<BR>\n" );
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document.write( "Do you see the middle term 11w?\r<BR>\n" );
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document.write( "I am interested in the coefficient of w or 11.\r<BR>\n" );
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document.write( "What two numbers when multiplied together will yield -80 but when added will yield 11?\r<BR>\n" );
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document.write( "How about 16 times -5?\r<BR>\n" );
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document.write( "Yes, 16 times -5 = -80 but when added 16 PLUS -5 = 11.\r<BR>\n" );
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document.write( "Are you following?\r<BR>\n" );
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document.write( "We now have this equation:\r<BR>\n" );
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document.write( "4w^2 + 16w - 5w - 20 = 0\r<BR>\n" );
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document.write( "We create two groups.\r<BR>\n" );
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document.write( "Let 4w^2 + 16w be Group A.\r<BR>\n" );
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document.write( "Let - 5w - 20 be Group B.\r<BR>\n" );
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document.write( "Factor each group individually or one at a time.\r<BR>\n" );
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document.write( "4w^2 + 16w becomes 4w(w + 4).\r<BR>\n" );
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document.write( "-5w - 20 becomes -5(w + 4).\r<BR>\n" );
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document.write( "We now have this set of factors:\r<BR>\n" );
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document.write( "(4w - 5) (w + 4) (w + 4) = 0\r<BR>\n" );
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document.write( "Do you see the quantity (w + 4)?\r<BR>\n" );
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document.write( "We only need one of them.\r<BR>\n" );
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document.write( "We are left with two factors:\r<BR>\n" );
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document.write( "(4w - 5) (w + 4) = 0\r<BR>\n" );
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document.write( "Set each factor = 0 and solve for w.\r<BR>\n" );
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document.write( "4w - 5 = 0\r<BR>\n" );
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document.write( "4w = 5\r<BR>\n" );
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document.write( "w = 5/4\r<BR>\n" );
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document.write( "Do the same with the other factor.\r<BR>\n" );
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document.write( "w + 4 = 0\r<BR>\n" );
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document.write( "w = -4\r<BR>\n" );
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document.write( "Final answer: w = 5/4 and w = -4\r<BR>\n" );
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document.write( "Did you follow?\r<BR>\n" );
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