document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=144532>Question 144532</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help solving this word problem which I'm supposed to solve using a quadratic equation.  Any help would be appreciated.  thanks.\r<BR>\n" );
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document.write( "A designer attempts to arrange the characters of his artwork in the form of a square grid with equal numbers of rows and columns, but finds that 24 characters are left out. When he tries to add one more row and column, he finds that he has 25 too few characters. Find the number of characters used by the designer. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #105275 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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/cgi-bin/show-face.mpl?user=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=105275\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> He has n characters.<BR>\n" );
document.write( "If he makes it x by x, he has 24 left over, so n = x^2+24<BR>\n" );
document.write( "If he makes it (x+1) by (x+1), he's 25 short, so n = (x+1)^2 - 25<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+%28x%2B1%29%5E2+-+25 ALIGN=MIDDLE  ALT=\"n+=+%28x%2B1%29%5E2+-+25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+x%5E2%2B24 ALIGN=MIDDLE  ALT=\"n+=+x%5E2%2B24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B24+=+%28x%2B1%29%5E2+-+25 ALIGN=MIDDLE  ALT=\"x%5E2%2B24+=+%28x%2B1%29%5E2+-+25\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Since both equal n<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B24+=+x%5E2%2B2x%2B1+-+25 ALIGN=MIDDLE  ALT=\"x%5E2%2B24+=+x%5E2%2B2x%2B1+-+25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24+=+2x-24 ALIGN=MIDDLE  ALT=\"24+=+2x-24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2x = 48<BR>\n" );
document.write( "x = 24\r<BR>\n" );
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document.write( "n = 24*24 + 24 = 600<BR>\n" );
document.write( "25*25 is 625, so he would be 25 short.\r<BR>\n" );
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document.write( "There was no need to solve a quadratic.<BR>\n" );
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