document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=713829>Question 713829</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the equation by completing the square to obtain exact solutions.\r<BR>\n" );
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document.write( "* w^2 + 10w + 25 = 1/4\r<BR>\n" );
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document.write( "* What I've tried :  w^2+ 10w = 1/4 - 25 \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #438653 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=438653\">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=w%5E2+%2B+10w+%2B+25+=+1%2F4 ALIGN=MIDDLE  ALT=\"w%5E2+%2B+10w+%2B+25+=+1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtracting 25 like you tried is the normal step at this point. So it is not an incorrect thing to do. But if you look ahead at the next steps you will see that it is unnecessary. The next steps would be:<ol><li>Find 1/2 of 10 (which would be 5)</li><li>Square the 5 (which would be 25)</li><li>Add the square to each side</li></ol>These steps would just bring us back to where we started!? This means that the trinomial we started with is already a perfect square trinomial! We can just go directly from:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2+%2B+10w+%2B+25+=+1%2F4 ALIGN=MIDDLE  ALT=\"w%5E2+%2B+10w+%2B+25+=+1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28w%2B5%29%5E2+=+1%2F4 ALIGN=MIDDLE  ALT=\"%28w%2B5%29%5E2+=+1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Now that the square has been completed we can solve the equation. Finding the square root of each side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28w%2B5%29%5E2%29+=+sqrt%281%2F4%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28w%2B5%29%5E2%29+=+sqrt%281%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which, remembering the positive and negative square roots, gives us:<BR>\n" );
document.write( "w + 5 = <u>+</u><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Adding -5 to each side we get:<BR>\n" );
document.write( "w = -5 <u>+</u><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which is short for:<BR>\n" );
document.write( "w = -5 + 1/2 or w = -5 - 1/2<BR>\n" );
document.write( "which simplify to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+-4%261%2F2 ALIGN=MIDDLE  ALT=\"w+=+-4%261%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+-5%261%2F2 ALIGN=MIDDLE  ALT=\"w+=+-5%261%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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