document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=548975>Question 548975</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve the equation by completeing the square:\r<BR>\n" );
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document.write( "7x^2+10x=-2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #357384 by </B><A HREF=/tutors/aboutme.mpl?userid=mathie123><B>mathie123(224)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathie123><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=357384\">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=7x%5E2%2B10x=-2 ALIGN=MIDDLE  ALT=\"7x%5E2%2B10x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We will first put everything on one side of the equation (as in most classes, students are most familiar with completely the square when it is in the form ax^2+bx+c\r<BR>\n" );
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document.write( "this gives us:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%5E2%2B10x%2B2=0 ALIGN=MIDDLE  ALT=\"7x%5E2%2B10x%2B2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we need to make the constant in front of x^2 1, so we will factor out a 7 from our first two terms:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%28x%5E2%2B10%2F7%2Ax%29%2B2=0 ALIGN=MIDDLE  ALT=\"7%28x%5E2%2B10%2F7%2Ax%29%2B2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now the rules for completing the square say we must take the constant in front of the x and square one half of this number and add and subtract this number.  \r<BR>\n" );
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document.write( "So our constant is 10/7.  One half of 10/7 is <BR>\n" );
document.write( "10/7*1/2=10/14<BR>\n" );
document.write( "and this squared is <BR>\n" );
document.write( "(10/14)^2=(5/7)^2=25/49\r<BR>\n" );
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document.write( "So we will add and subtract this number (so essentially we are adding 0 to our equation, which does not change it). <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%28x%5E2%2B10%2F7%2Ax%2B25%2F49-25%2F49%29%2B2=0 ALIGN=MIDDLE  ALT=\"7%28x%5E2%2B10%2F7%2Ax%2B25%2F49-25%2F49%29%2B2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We will now take our -25/49 out of the bracket (remembering to multiply it by 7 when we take it out).  this leaves:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%28x%5E2%2B10%2F7%2Ax%2B25%2F49%29%2B2-25%2F49%2A7=0 ALIGN=MIDDLE  ALT=\"7%28x%5E2%2B10%2F7%2Ax%2B25%2F49%29%2B2-25%2F49%2A7=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Almost there.... <BR>\n" );
document.write( "We will complete the square inside of the brackets.  Essentially we just write it in the form (x+a)^2 where a is 1/2 of the constant in front of the x term originally (we found this was 10/14=5/7\r<BR>\n" );
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document.write( "So we have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%28x%2B5%2F7%29%5E2%2B2-25%2F7=0 ALIGN=MIDDLE  ALT=\"7%28x%2B5%2F7%29%5E2%2B2-25%2F7=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%28x%2B5%2F7%29%5E2%2B14%2F7-25%2F7=0 ALIGN=MIDDLE  ALT=\"7%28x%2B5%2F7%29%5E2%2B14%2F7-25%2F7=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%28x%2B5%2F7%29%5E2-11%2F7=0 ALIGN=MIDDLE  ALT=\"7%28x%2B5%2F7%29%5E2-11%2F7=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now it is just solving for x, so let's isolate x:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%28x%2B5%2F7%29%5E2-11%2F7=0 ALIGN=MIDDLE  ALT=\"7%28x%2B5%2F7%29%5E2-11%2F7=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%28x%2B5%2F7%29%5E2=11%2F7 ALIGN=MIDDLE  ALT=\"7%28x%2B5%2F7%29%5E2=11%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%28x%2B5%2F7%29%5E2%2F7=%2811%2F7%29%2F7 ALIGN=MIDDLE  ALT=\"7%28x%2B5%2F7%29%5E2%2F7=%2811%2F7%29%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B5%2F7%29%5E2=11%2F49 ALIGN=MIDDLE  ALT=\"%28x%2B5%2F7%29%5E2=11%2F49\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B5%2F7%29=%2B-sqrt%2811%2F49%29 ALIGN=MIDDLE  ALT=\"%28x%2B5%2F7%29=%2B-sqrt%2811%2F49%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2B-sqrt%2811%2F49%29-5%2F7 ALIGN=MIDDLE  ALT=\"x=%2B-sqrt%2811%2F49%29-5%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This can be simplified on your calculator... but I will leave that to you.  <BR>\n" );
document.write( "Hopefully this helps... let me know if you are still unsure. <BR>\n" );
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