document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=630719>Question 630719</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve for x/complete the square: 5x^2+2x&#8730;10=1? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #397100 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=397100\">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=5x%5E2%2B2xsqrt%2810%29=1 ALIGN=MIDDLE  ALT=\"5x%5E2%2B2xsqrt%2810%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "First I am going to use the Commutative and Associative Properties on the middle term so that it is something times x, with the x at the end:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2%2B%282sqrt%2810%29%29x=1 ALIGN=MIDDLE  ALT=\"5x%5E2%2B%282sqrt%2810%29%29x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "It is easier to complete a square if the coefficient of the squared term is 1. So we will divide both sides by 5 (or multiply by 1/5):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%282sqrt%2810%29%2F5%29x=1%2F5 ALIGN=MIDDLE  ALT=\"x%5E2%2B%282sqrt%2810%29%2F5%29x=1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Next we find half of the middle coefficient. Half of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%2810%29%2F5 ALIGN=MIDDLE  ALT=\"2sqrt%2810%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2810%29%2F5 ALIGN=MIDDLE  ALT=\"sqrt%2810%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Next we square the \"half\" and add that number to both sides. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%2810%29%2F5%29%5E2+=+10%2F25+=+2%2F5 ALIGN=MIDDLE  ALT=\"%28sqrt%2810%29%2F5%29%5E2+=+10%2F25+=+2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Adding 2/5 to each side we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%282sqrt%2810%29%2F5%29x%2B2%2F5=1%2F5%2B2%2F5 ALIGN=MIDDLE  ALT=\"x%5E2%2B%282sqrt%2810%29%2F5%29x%2B2%2F5=1%2F5%2B2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplifies to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%282sqrt%2810%29%2F5%29x%2B2%2F5=3%2F5 ALIGN=MIDDLE  ALT=\"x%5E2%2B%282sqrt%2810%29%2F5%29x%2B2%2F5=3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The left side is a completed square after what we have done. It is (x + the \"half\" we found earlier) squared:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Bsqrt%2810%29%2F5%29%5E2=3%2F5 ALIGN=MIDDLE  ALT=\"%28x%2Bsqrt%2810%29%2F5%29%5E2=3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we find the square root of each side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28x%2Bsqrt%2810%29%2F5%29%5E2%29=sqrt%283%2F5%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28x%2Bsqrt%2810%29%2F5%29%5E2%29=sqrt%283%2F5%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%2Bsqrt%2810%29%2F5 ALIGN=MIDDLE  ALT=\"x%2Bsqrt%2810%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <u>+</u><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%2F5%29 ALIGN=MIDDLE  ALT=\"sqrt%283%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Rationalizing the denominator on the right:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Bsqrt%2810%29%2F5 ALIGN=MIDDLE  ALT=\"x%2Bsqrt%2810%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <u>+</u><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%283%2F5%29%285%2F5%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28%283%2F5%29%285%2F5%29%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%2Bsqrt%2810%29%2F5 ALIGN=MIDDLE  ALT=\"x%2Bsqrt%2810%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <u>+</u><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2815%2F25%29 ALIGN=MIDDLE  ALT=\"sqrt%2815%2F25%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%2Bsqrt%2810%29%2F5 ALIGN=MIDDLE  ALT=\"x%2Bsqrt%2810%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <u>+</u><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2815%29%2Fsqrt%2825%29 ALIGN=MIDDLE  ALT=\"sqrt%2815%29%2Fsqrt%2825%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%2Bsqrt%2810%29%2F5 ALIGN=MIDDLE  ALT=\"x%2Bsqrt%2810%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <u>+</u><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2815%29%2F5 ALIGN=MIDDLE  ALT=\"sqrt%2815%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Adding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%2810%29%2F5 ALIGN=MIDDLE  ALT=\"-sqrt%2810%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to each side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-sqrt%2810%29%2F5+%2B-+sqrt%2815%29%2F5%29 ALIGN=MIDDLE  ALT=\"x+=+-sqrt%2810%29%2F5+%2B-+sqrt%2815%29%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplifies to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-sqrt%2810%29+%2B-+sqrt%2815%29%29%2F5%29 ALIGN=MIDDLE  ALT=\"x+=+%28-sqrt%2810%29+%2B-+sqrt%2815%29%29%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );