document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118906>Question 118906</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve for  x   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2-6x-160=0+ ALIGN=MIDDLE  ALT=\"+x%5E2-6x-160=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #87006 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=87006\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given to solve:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2-6x-160=0+ ALIGN=MIDDLE  ALT=\"+x%5E2-6x-160=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This equation can be solved by factoring. Look for factors of -160 that can be combined to <BR>\n" );
document.write( "give -6. If you think about this -160 can be factored to -16 and + 10. If these two numbers<BR>\n" );
document.write( "are added the result is -6. Using this information you can factor the left side of the equation<BR>\n" );
document.write( "to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+16%29%2A%28x+%2B+10%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+-+16%29%2A%28x+%2B+10%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "If you multiply out the two factors on left side you will get the given equation ... which is <BR>\n" );
document.write( "as it should be.<BR>\n" );
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document.write( "If either of the factors is equal to zero, the equation will be true ... because a multiplication<BR>\n" );
document.write( "by zero on the left side will make the entire left side equal to zero and therefore, the<BR>\n" );
document.write( "left side will equal the zero on the right side.<BR>\n" );
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document.write( "So let's set each of the factors equal to zero and this will make the equation true.<BR>\n" );
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document.write( "First:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+16+=+0 ALIGN=MIDDLE  ALT=\"x+-+16+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Add 16 to both sides of this equation and you get for x:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+16 ALIGN=MIDDLE  ALT=\"x+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Next set the other factor equal to zero:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+10+=+0 ALIGN=MIDDLE  ALT=\"+x+%2B+10+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Subtract 10 from both sides and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-10 ALIGN=MIDDLE  ALT=\"x+=+-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So you have two solutions for x ... x = 16 and x = -10. You can check these two answers by<BR>\n" );
document.write( "returning to the original (given) equation and substituting each of these answers for<BR>\n" );
document.write( "x to see if they make the left side of the equation become zero and therefore equal to the<BR>\n" );
document.write( "right side.<BR>\n" );
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document.write( "The given equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+6x+-+160+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+6x+-+160+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Letting x be 16 makes the left side:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%5E2+-+6%2816%29+-+160+=+256+-+96+-+160+=+256+-+256+=+0 ALIGN=MIDDLE  ALT=\"16%5E2+-+6%2816%29+-+160+=+256+-+96+-+160+=+256+-+256+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Next let x be -10 makes the left side:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-10%29%5E2+-6%28-10%29+-+160+=+100+%2B+60+-+160+=+160+-+160+=+0 ALIGN=MIDDLE  ALT=\"%28-10%29%5E2+-6%28-10%29+-+160+=+100+%2B+60+-+160+=+160+-+160+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So for either value of x (16 and -10) the left side of the given equation becomes zero<BR>\n" );
document.write( "and therefore equal to the right side of the equation ... making the equation true. <BR>\n" );
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document.write( "This means that the two answers we found are correct.<BR>\n" );
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document.write( "Hope this helps you to understand this problem and one way that it can be solved (factoring).<BR>\n" );
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