document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=156156>Question 156156</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if x^2+6x+16=(x+a)^2+b for all values of x, find the values of a and b </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #115019 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=115019\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B6x%2B16=%28x%2Ba%29%5E2%2Bb ALIGN=MIDDLE  ALT=\"x%5E2%2B6x%2B16=%28x%2Ba%29%5E2%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B6x%2B16=x%5E2%2B2ax%2Ba%5E2%2Bb ALIGN=MIDDLE  ALT=\"x%5E2%2B6x%2B16=x%5E2%2B2ax%2Ba%5E2%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B16=2ax%2Ba%5E2%2Bb ALIGN=MIDDLE  ALT=\"6x%2B16=2ax%2Ba%5E2%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides\r<BR>\n" );
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document.write( "Notice how the term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ax ALIGN=MIDDLE  ALT=\"2ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the <b>only</b> term on the right side that has an \"x\" in it. So this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x=2ax ALIGN=MIDDLE  ALT=\"6x=2ax\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x=2ax ALIGN=MIDDLE  ALT=\"6x=2ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=a ALIGN=MIDDLE  ALT=\"3=a\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x ALIGN=MIDDLE  ALT=\"2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate \"a\"\r<BR>\n" );
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document.write( "So the first answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=3 ALIGN=MIDDLE  ALT=\"a=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "-------------------------\r<BR>\n" );
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document.write( "Looking back at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B16=2ax%2Ba%5E2%2Bb ALIGN=MIDDLE  ALT=\"6x%2B16=2ax%2Ba%5E2%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the terms <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb ALIGN=MIDDLE  ALT=\"a%5E2%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > do not have an \"x\" term in them at all. So this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16=a%5E2%2Bb ALIGN=MIDDLE  ALT=\"16=a%5E2%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16=a%5E2%2Bb ALIGN=MIDDLE  ALT=\"16=a%5E2%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16=3%5E2%2Bb ALIGN=MIDDLE  ALT=\"16=3%5E2%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16=9%2Bb ALIGN=MIDDLE  ALT=\"16=9%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 3 to get 9\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7=b ALIGN=MIDDLE  ALT=\"7=b\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 9 from both sides\r<BR>\n" );
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document.write( "So the second answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=7 ALIGN=MIDDLE  ALT=\"b=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=3 ALIGN=MIDDLE  ALT=\"a=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=7 ALIGN=MIDDLE  ALT=\"b=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B6x%2B16=%28x%2Ba%29%5E2%2Bb ALIGN=MIDDLE  ALT=\"x%5E2%2B6x%2B16=%28x%2Ba%29%5E2%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2%2B6x%2B16=%28x%2B3%29%5E2%2B7 ALIGN=MIDDLE  ALT=\"+x%5E2%2B6x%2B16=%28x%2B3%29%5E2%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2%2B6x%2B16=x%5E2%2B6x%2B16 ALIGN=MIDDLE  ALT=\"+x%5E2%2B6x%2B16=x%5E2%2B6x%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=0 ALIGN=MIDDLE  ALT=\"0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > works\r<BR>\n" );
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