document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=61003>Question 61003</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0072538953/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Can somebody please help me! \r<BR>\n" );
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document.write( "Find all real solutions to \r<BR>\n" );
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document.write( "(a) x^2 + x + SQRT(x^2 + x) - 2 = 0 \r<BR>\n" );
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document.write( "I have been working on this problems for a couple of days and I can't seem to understand, or even know what to do. I know I need to use the substitution methods but the radical in the equation is confusing me. <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 #41937 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=41937\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find all real solutions to \r<BR>\n" );
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document.write( "(a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bx%2Bsqrt%28x%5E2%2Bx%29-2=0 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx%2Bsqrt%28x%5E2%2Bx%29-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Use the substitution method.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28x%5E2%2Bx%29%29%5E2%2Bsqrt%28x%5E2%2Bx%29-2=0 ALIGN=MIDDLE  ALT=\"%28sqrt%28x%5E2%2Bx%29%29%5E2%2Bsqrt%28x%5E2%2Bx%29-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=sqrt%28x%5E2%2Bx%29 ALIGN=MIDDLE  ALT=\"P=sqrt%28x%5E2%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5E2%2BP-2=0 ALIGN=MIDDLE  ALT=\"P%5E2%2BP-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Factor<BR>\n" );
document.write( "(P+2)(P-1)=0<BR>\n" );
document.write( "P+2=0 and P-1=0<BR>\n" );
document.write( "P=-2 and P=1<BR>\n" );
document.write( "But we want to know what x is, so let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2%2Bx%29=P ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2%2Bx%29=P\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2%2Bx%29=-2 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2%2Bx%29=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2%2Bx%29=1 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2%2Bx%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28x%5E2%2Bx%29%29%5E2=%28-2%29%5E2 ALIGN=MIDDLE  ALT=\"%28sqrt%28x%5E2%2Bx%29%29%5E2=%28-2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28x%5E2%2Bx%29%29%5E2=1%5E2 ALIGN=MIDDLE  ALT=\"%28sqrt%28x%5E2%2Bx%29%29%5E2=1%5E2\"   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=4 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <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%5E2%2Bx-4=0 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx-4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bx-1=0 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "You have to use the quadratic equation to solve these:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "when a=1, b=1, c=-4<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-1%2B-sqrt%28%281%29%5E2-4%281%29%28-4%29%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x=%28-1%2B-sqrt%28%281%29%5E2-4%281%29%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%281%2B16%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%28-1%2B-sqrt%281%2B16%29%29%2F2\"   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%2817%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%28-1%2B-sqrt%2817%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  You have to check these to see if they are valid or extraneous.  I checked these by plugging them into my calculator and the were both extraneous.<BR>\n" );
document.write( "when a=1, b=1, and c=-1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-1%2B-sqrt%28%281%29%5E2-4%281%29%28-1%29%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x=%28-1%2B-sqrt%28%281%29%5E2-4%281%29%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=highlight%28x=%28-1%2B-sqrt%285%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"highlight%28x=%28-1%2B-sqrt%285%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  You have to check these to see if they are valid or extraneous.  I checked these with my calculator and they were both valid.<BR>\n" );
document.write( "If you have a TI-83 or 84, I can give you instructions on checking for extraneous solutions if you ask.<BR>\n" );
document.write( "Happy Calculating!!! </SPAN>\n" );
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