document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=315243>Question 315243</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bx%2B+sqrt%28x%5E2%2Bx%29-2=0 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx%2B+sqrt%28x%5E2%2Bx%29-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #225535 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=225535\">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=x%5E2%2Bx%2B+sqrt%28x%5E2%2Bx%29-2=0 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx%2B+sqrt%28x%5E2%2Bx%29-2=0\"   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%2Bx-2=-sqrt%28x%5E2%2Bx%29 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx-2=-sqrt%28x%5E2%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Square both sides,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4%2B2x%5E3-3x%5E2-4x%2B4=x%5E2%2Bx ALIGN=MIDDLE  ALT=\"x%5E4%2B2x%5E3-3x%5E2-4x%2B4=x%5E2%2Bx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4%2B2x%5E3-4x%5E2-5x%2B4=0 ALIGN=MIDDLE  ALT=\"x%5E4%2B2x%5E3-4x%5E2-5x%2B4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can factor this equation into the product of two quadratics,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2Bx-4%29%28x%5E2%2Bx-1%29=0 ALIGN=MIDDLE  ALT=\"%28x%5E2%2Bx-4%29%28x%5E2%2Bx-1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use the quadratic formula to find the roots of each quadratic.<BR>\n" );
document.write( "First solution:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bx-4 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%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+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A1%2A%28-4%29+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A1%2A%28-4%29+%29%29%2F%282%2A1%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+=+%28-1+%2B-+sqrt%28+17%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-1+%2B-+sqrt%28+17%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
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document.write( "Second solution:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bx-1 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%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+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A1%2A%28-1%29+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A1%2A%28-1%29+%29%29%2F%282%2A1%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+=+%28-1+%2B-+sqrt%28+5%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-1+%2B-+sqrt%28+5%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
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document.write( "Verify the solutions. <BR>\n" );
document.write( "The first set of solutions does not satisfy the equation for reasons having to do with the +/- feature relating to the square root. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%5E2%29=0+%2B-+a ALIGN=MIDDLE  ALT=\"sqrt%28a%5E2%29=0+%2B-+a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
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document.write( "The second set of solutions does satisfy the equation. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x+=+%28-1+%2B-+sqrt%28+5%29%29%2F2%29+ ALIGN=MIDDLE  ALT=\"highlight%28x+=+%28-1+%2B-+sqrt%28+5%29%29%2F2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or approximately,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0.611 ALIGN=MIDDLE  ALT=\"x=0.611\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1.611 ALIGN=MIDDLE  ALT=\"x=-1.611\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
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document.write( "We can also verify by graphing the function, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bx%2B+sqrt%28x%5E2%2Bx%29-2 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx%2B+sqrt%28x%5E2%2Bx%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and noting where it crosses the x-axis.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-2%2C+2%2C+-2%2C+2%2C+x%5E2%2Bx%2B+sqrt%28x%5E2%2Bx%29-2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-2%2C+2%2C+-2%2C+2%2C+x%5E2%2Bx%2B+sqrt%28x%5E2%2Bx%29-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );