document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=75813>Question 75813</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve for x by completing the square: x^2+6x=2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #54443 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=54443\">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=2 ALIGN=MIDDLE  ALT=\"x%5E2%2B6x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The process goes as follows:<BR>\n" );
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document.write( "First look at the coefficient or multiplier of the x term.  Take half of that coefficient,<BR>\n" );
document.write( "square the result, and add that number to both sides of the equation.<BR>\n" );
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document.write( "For this problem, the coefficient of the x term is +6. Take half of that and you have +3.<BR>\n" );
document.write( "Square the +3 and you get +9.  Add +9 to both sides of the equation to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+6x+%2B+9+=+2+%2B+9 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+6x+%2B+9+=+2+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You have now made the left side of the equation a perfect square.  The term that is squared<BR>\n" );
document.write( "is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+3%29 ALIGN=MIDDLE  ALT=\"%28x+%2B+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where the +3 comes from half the coefficient of the x term.  So the equation<BR>\n" );
document.write( "can be written as:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%5E2+=+11 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%5E2+=+11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Note that the 11 comes from adding the 2 and 9 on the right side.<BR>\n" );
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document.write( "Now take the square root of 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=x+%2B+3+=+%2Bsqrt%2811%29 ALIGN=MIDDLE  ALT=\"x+%2B+3+=+%2Bsqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3+=+-sqrt%2811%29 ALIGN=MIDDLE  ALT=\"x%2B3+=+-sqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Finally, subtract 3 from both sides to get rid of the +3 that is on the left side. When<BR>\n" );
document.write( "you do you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3%2Bsqrt%2811%29 ALIGN=MIDDLE  ALT=\"x+=+-3%2Bsqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3-sqrt%2811%29 ALIGN=MIDDLE  ALT=\"x+=+-3-sqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and those are the two values of x that satisfy the equation of the original problem. <BR>\n" );
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document.write( "Hope this helps you to see and understand the process that you use to solve quadratic <BR>\n" );
document.write( "equations by completing the square. The process remains the same, only the numbers<BR>\n" );
document.write( "change for different quadratic equations. </SPAN>\n" );
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