document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=621853>Question 621853</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help solve the equation (20-x)^2+(20+x)^2=8 including the smaller and larger values of x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #391043 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=391043\">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=%2820-x%29%5E2%2B%2820%2Bx%29%5E2=8 ALIGN=MIDDLE  ALT=\"%2820-x%29%5E2%2B%2820%2Bx%29%5E2=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving equations often starts with simplifying each side of the equation. We can use FOIL or patterns to square the binomials on the left side. (I like using the patterns.)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820%29%5E2-2%2820%29%28x%29%2B%28x%29%5E2+%2B+%2820%29%5E2%2B2%2820%29%28x%29%2B%28x%29%5E2+=+8 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplifies as follows:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400-40x%2Bx%5E2+%2B+400%2B40x%2Bx%5E2+=+8 ALIGN=MIDDLE  ALT=\"400-40x%2Bx%5E2+%2B+400%2B40x%2Bx%5E2+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+%2B+800+=+8 ALIGN=MIDDLE  ALT=\"2x%5E2+%2B+800+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "This is a quadratic equation. It has no \"x term\" in it so probably the easiest way to solve this is to isolate the squared term and find a square root. Subtracting 800 from each side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+=+-792 ALIGN=MIDDLE  ALT=\"2x%5E2+=+-792\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and then dividing by 2:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+-396 ALIGN=MIDDLE  ALT=\"x%5E2+=+-396\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Normally we would now find the square root of each side. But if we look at what we have we will realize that there is no solution to this equation because <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;\" > cannot turn out to be a negative number, like -796 (unless x is a complex number).<br><BR>\n" );
document.write( "If you know about complex numbers and if you are supposed to find complex solutions to this equation, we can continue:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2%29+=+sqrt%28-796%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2%29+=+sqrt%28-796%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+=+sqrt%28-796%29 ALIGN=MIDDLE  ALT=\"x+=+sqrt%28-796%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-sqrt%28-796%29 ALIGN=MIDDLE  ALT=\"x+=+-sqrt%28-796%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "With a negative number in the square root, we start by factoring out -1:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+sqrt%28-1%2A796%29 ALIGN=MIDDLE  ALT=\"x+=+sqrt%28-1%2A796%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-sqrt%28-1%2A796%29 ALIGN=MIDDLE  ALT=\"x+=+-sqrt%28-1%2A796%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+=+sqrt%28-1%29%2Asqrt%28796%29 ALIGN=MIDDLE  ALT=\"x+=+sqrt%28-1%29%2Asqrt%28796%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-sqrt%28-1%29%2Asqrt%28796%29 ALIGN=MIDDLE  ALT=\"x+=+-sqrt%28-1%29%2Asqrt%28796%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+=+i%2Asqrt%28796%29 ALIGN=MIDDLE  ALT=\"x+=+i%2Asqrt%28796%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-i%2Asqrt%28796%29 ALIGN=MIDDLE  ALT=\"x+=+-i%2Asqrt%28796%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we simplify the remaining square root by finding perfect square factors:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+i%2Asqrt%284%2A199%29 ALIGN=MIDDLE  ALT=\"x+=+i%2Asqrt%284%2A199%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-i%2Asqrt%284%2A199%29 ALIGN=MIDDLE  ALT=\"x+=+-i%2Asqrt%284%2A199%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+=+i%2Asqrt%284%29%2Asqrt%28199%29 ALIGN=MIDDLE  ALT=\"x+=+i%2Asqrt%284%29%2Asqrt%28199%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-i%2Asqrt%284%29%2Asqrt%28199%29 ALIGN=MIDDLE  ALT=\"x+=+-i%2Asqrt%284%29%2Asqrt%28199%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+=+i%2A2%2Asqrt%28199%29 ALIGN=MIDDLE  ALT=\"x+=+i%2A2%2Asqrt%28199%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-i%2A2%2Asqrt%28199%29 ALIGN=MIDDLE  ALT=\"x+=+-i%2A2%2Asqrt%28199%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2i%2Asqrt%28199%29 ALIGN=MIDDLE  ALT=\"x+=+2i%2Asqrt%28199%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-2i%2Asqrt%28199%29 ALIGN=MIDDLE  ALT=\"x+=+-2i%2Asqrt%28199%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "These are the only (complex) solutions to your equation. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );