document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=266245>Question 266245</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If 3x^2-12x+14=3(x+p)^2+q, what are the values of p and q? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #195679 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20060)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=195679\">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=3x%5E2-12x%2B14=3%28x%2Bp%29%5E2%2Bq ALIGN=MIDDLE  ALT=\"3x%5E2-12x%2B14=3%28x%2Bp%29%5E2%2Bq\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since it must be identically true regardless of the value of x, <BR>\n" );
document.write( "the easy way is to substitute any two values of x and solve the <BR>\n" );
document.write( "resulting system:\r<BR>\n" );
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document.write( "Substitute x=0\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%280%29%5E2-12%280%29%2B14=3%28%280%29%2Bp%29%5E2%2Bq ALIGN=MIDDLE  ALT=\"3%280%29%5E2-12%280%29%2B14=3%28%280%29%2Bp%29%5E2%2Bq\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14=3p%5E2%2Bq ALIGN=MIDDLE  ALT=\"14=3p%5E2%2Bq\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substitute x=1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%281%29%5E2-12%281%29%2B14=3%28%281%29%2Bp%29%5E2%2Bq ALIGN=MIDDLE  ALT=\"3%281%29%5E2-12%281%29%2B14=3%28%281%29%2Bp%29%5E2%2Bq\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-12%2B14=3%281%2Bp%29%5E2%2Bq ALIGN=MIDDLE  ALT=\"3-12%2B14=3%281%2Bp%29%5E2%2Bq\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5=3%281%2Bp%29%5E2%2Bq ALIGN=MIDDLE  ALT=\"5=3%281%2Bp%29%5E2%2Bq\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So we have this system of equations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%2814=3p%5E2%2Bq%2C5=3%281%2Bp%29%5E2%2Bq%29 ALIGN=MIDDLE  ALT=\"system%2814=3p%5E2%2Bq%2C5=3%281%2Bp%29%5E2%2Bq%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solve both for q:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28q=14-3p%5E2%2Cq=5-3%281%2Bp%29%5E2%29 ALIGN=MIDDLE  ALT=\"system%28q=14-3p%5E2%2Cq=5-3%281%2Bp%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Set their right sides equal and solve\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14-3p%5E2=5-3%281%2Bp%29%5E2 ALIGN=MIDDLE  ALT=\"14-3p%5E2=5-3%281%2Bp%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplify and solve this and you'll get <BR>\n" );
document.write( "one solution <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=-2 ALIGN=MIDDLE  ALT=\"p=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then substitute <BR>\n" );
document.write( "that into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q=14-3p%5E2 ALIGN=MIDDLE  ALT=\"q=14-3p%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q=14-3%28-2%29%5E2=14-3%284%29=14-12=2 ALIGN=MIDDLE  ALT=\"q=14-3%28-2%29%5E2=14-3%284%29=14-12=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Edwin</pre>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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