document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=183200>Question 183200</A>: <I><SPAN STYLE=\"word-break: break-all;\"> \"suppose x^2+a^2x+a^2 factors into (x+a)^2. what is the value of a, that is not zero?\" </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #137554 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=137554\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since we're supposing that \"x^2+a^2x+a^2 factors into (x+a)^2\", this means that \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Ba%5E2x%2Ba%5E2=%28x%2Ba%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2Ba%5E2x%2Ba%5E2=%28x%2Ba%29%5E2\"   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%2Ba%5E2x%2Ba%5E2=%28x%2Ba%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2Ba%5E2x%2Ba%5E2=%28x%2Ba%29%5E2\"   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%2Ba%5E2x%2Ba%5E2=x%5E2%2B2ax%2Ba%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2Ba%5E2x%2Ba%5E2=x%5E2%2B2ax%2Ba%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28x%5E2-x%5E2%29%2Ba%5E2x%2Ba%5E2=cross%28x%5E2-x%5E2%29%2B2ax%2Ba%5E2 ALIGN=MIDDLE  ALT=\"cross%28x%5E2-x%5E2%29%2Ba%5E2x%2Ba%5E2=cross%28x%5E2-x%5E2%29%2B2ax%2Ba%5E2\"   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. Note: the <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;\" > terms cancel out.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2x%2Bcross%28a%5E2-a%5E2%29=2ax%2Bcross%28a%5E2-a%5E2%29 ALIGN=MIDDLE  ALT=\"a%5E2x%2Bcross%28a%5E2-a%5E2%29=2ax%2Bcross%28a%5E2-a%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2 ALIGN=MIDDLE  ALT=\"a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides. Note: the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2 ALIGN=MIDDLE  ALT=\"a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > terms cancel out.\r<BR>\n" );
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document.write( "So we're left with: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5E2%2Across%28x%29%29%2Fcross%28x%29=%282a%2Across%28x%29%29%2Fcross%28x%29 ALIGN=MIDDLE  ALT=\"%28a%5E2%2Across%28x%29%29%2Fcross%28x%29=%282a%2Across%28x%29%29%2Fcross%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by \"x\". Once again, the \"x\" terms cancel\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=2a ALIGN=MIDDLE  ALT=\"a%5E2=2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2-2a=0 ALIGN=MIDDLE  ALT=\"a%5E2-2a=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 2a from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28a-2%29=0 ALIGN=MIDDLE  ALT=\"a%28a-2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the left side \r<BR>\n" );
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document.write( "Now set each factor equal to zero:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=0 ALIGN=MIDDLE  ALT=\"a=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-2=0 ALIGN=MIDDLE  ALT=\"a-2=0\"   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=a=0 ALIGN=MIDDLE  ALT=\"a=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >    Now solve for \"a\" in each case\r<BR>\n" );
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document.write( "Note: since we want a value of \"a\" \"that is not zero\", this means that we'll ignore the value <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=0 ALIGN=MIDDLE  ALT=\"a=0\"   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 solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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