document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=114754>Question 114754</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can some one help me please. <BR>\n" );
document.write( "Solve by completing the square<BR>\n" );
document.write( "x^2 + 8x + 13 = 0\r<BR>\n" );
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document.write( "Thank you inadavance. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #83497 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=83497\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B8x%2B13=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B8x%2B13=0\"   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%2B8x=-13 ALIGN=MIDDLE  ALT=\"x%5E2%2B8x=-13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 13 from both sides\r<BR>\n" );
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document.write( "Take half of the x coefficient 8 to get 4 (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F2=4 ALIGN=MIDDLE  ALT=\"8%2F2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "Now square 4 to get 16 (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%29%5E2=16 ALIGN=MIDDLE  ALT=\"%284%29%5E2=16\"   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%2B8x%2B16=-13%2B16 ALIGN=MIDDLE  ALT=\"x%5E2%2B8x%2B16=-13%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add this result (16) to both sides. Now the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B8x%2B16 ALIGN=MIDDLE  ALT=\"x%5E2%2B8x%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a perfect square trinomial.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%5E2=-13%2B16 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%5E2=-13%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B8x%2B16 ALIGN=MIDDLE  ALT=\"x%5E2%2B8x%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (note: if you need help with factoring, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%5E2=3 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%5E2=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B4=0%2B-sqrt%283%29 ALIGN=MIDDLE  ALT=\"x%2B4=0%2B-sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4%2B-sqrt%283%29 ALIGN=MIDDLE  ALT=\"x=-4%2B-sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 4 from both sides to isolate x.\r<BR>\n" );
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document.write( "So the expression breaks down to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4%2Bsqrt%283%29 ALIGN=MIDDLE  ALT=\"x=-4%2Bsqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4-sqrt%283%29 ALIGN=MIDDLE  ALT=\"x=-4-sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our answer is approximately\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2.26794919243112 ALIGN=MIDDLE  ALT=\"x=-2.26794919243112\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5.73205080756888 ALIGN=MIDDLE  ALT=\"x=-5.73205080756888\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Here is visual proof\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2B8x%2B13%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2B8x%2B13%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2%2B8x%2B13 ALIGN=MIDDLE  ALT=\"y=x%5E2%2B8x%2B13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "When we use the root finder feature on a calculator, we would find that the x-intercepts are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2.26794919243112 ALIGN=MIDDLE  ALT=\"x=-2.26794919243112\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5.73205080756888 ALIGN=MIDDLE  ALT=\"x=-5.73205080756888\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so this verifies our answer.\r<BR>\n" );
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