document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=709676>Question 709676</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the whole number such that the twice its  square added to itself makes 10\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #436758 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=436758\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = the number<BR>\n" );
document.write( "Then...<BR>\n" );
document.write( "its square = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "twice its square = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax%5E2 ALIGN=MIDDLE  ALT=\"2%2Ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "twice its square added to itself = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax%5E2+%2B+x ALIGN=MIDDLE  ALT=\"2%2Ax%5E2+%2B+x\"   DISABLED_style= \"max-width:90%; height:auto;\" > (or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+2%2Ax%5E2 ALIGN=MIDDLE  ALT=\"x+%2B+2%2Ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<br><BR>\n" );
document.write( "So \"twice its  square added to itself makes 10\" translates into:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax%5E2+%2B+x+=+10 ALIGN=MIDDLE  ALT=\"2%2Ax%5E2+%2B+x+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we solve this equation for x.<br><BR>\n" );
document.write( "This is a quadratic equation so we want one side to be zero. Subtracting 10 from each side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax%5E2+%2B+x+-+10+=0 ALIGN=MIDDLE  ALT=\"2%2Ax%5E2+%2B+x+-+10+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Next we factor (or use the Quadratic Formula). This factors without too much difficulty:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B5%29%28x-2%29+=+0 ALIGN=MIDDLE  ALT=\"%282x%2B5%29%28x-2%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From the Zero Product Property we know that this product can be zero <i>only</i> if one (or more) of the factors is zero. So:<BR>\n" );
document.write( "2x+5 = 0 or x-2 = 0<BR>\n" );
document.write( "Solving these we should get:<BR>\n" );
document.write( "x = -5/2 or x = 2<br><BR>\n" );
document.write( "Since the problem asks for \"whole number\" solution we will reject -5/2. So the solution to your problem is 2. </SPAN>\n" );
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