document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=110062>Question 110062</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all solutions to the equation.<BR>\n" );
document.write( "r(squared)-8t=-15 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #80192 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=80192\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given the equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2+-8t+=+-15 ALIGN=MIDDLE  ALT=\"t%5E2+-8t+=+-15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Begin by collecting all the terms on the left side of the equation and getting a zero on the<BR>\n" );
document.write( "right side. You can do this by adding +15 to both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2+-8t+%2B+15+=+0 ALIGN=MIDDLE  ALT=\"t%5E2+-8t+%2B+15+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Note that the left side of this equation factors and after factoring the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28t+-+5%29%2A%28t+-+3%29=+0 ALIGN=MIDDLE  ALT=\"%28t+-+5%29%2A%28t+-+3%29=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This equation will be true if either of the two factors on the left side is equal to zero. <BR>\n" );
document.write( "This is the case because multiplication by zero on the left side makes the entire left<BR>\n" );
document.write( "side equal to zero ... and therefore, it is equal to the right side.<BR>\n" );
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document.write( "So, one at a time, set the two factors equal to zero to solve for t.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+-+5+=+0 ALIGN=MIDDLE  ALT=\"t+-+5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Add 5 to 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=t+=+5 ALIGN=MIDDLE  ALT=\"t+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Next:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+-+3+=+0 ALIGN=MIDDLE  ALT=\"t+-+3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Add 3 to 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=t+=+3 ALIGN=MIDDLE  ALT=\"t+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The two answers to this problem are t = 5 and t = 3. Let's check them by returning to<BR>\n" );
document.write( "the given equation, substituting these values, and seeing if the equation balances.<BR>\n" );
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document.write( "Start with:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2+-8t+=+-15 ALIGN=MIDDLE  ALT=\"t%5E2+-8t+=+-15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "First substitute 5 for t and the left side of the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E2+-+8%2A5+=+25+-+40+=+-15 ALIGN=MIDDLE  ALT=\"5%5E2+-+8%2A5+=+25+-+40+=+-15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So when t = 5 the left side of the equation becomes -15 and this equals the right side.<BR>\n" );
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document.write( "Next substitute 3 for t and the left side of the equation is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E2+-+8%2A3+=+9+-+24+=+-15 ALIGN=MIDDLE  ALT=\"3%5E2+-+8%2A3+=+9+-+24+=+-15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "As before, when t = 3 the left side of the equation is -15 and this equals the right side.<BR>\n" );
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document.write( "So we can conclude that t = 5 and t = 3 are the correct answers to this problem.<BR>\n" );
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document.write( "Hope this helps you to understand this problem.<BR>\n" );
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