document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=140321>Question 140321</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve by substitution \r<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 #102189 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=102189\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Start with the given equations\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2=26 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2=26\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%28-x%2B8%29%5E2=26 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28-x%2B8%29%5E2=26\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x%2B8 ALIGN=MIDDLE  ALT=\"y=-x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bx%5E2-16x%2B64=26 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx%5E2-16x%2B64=26\"   DISABLED_style= \"max-width:90%; height:auto;\" > Foil\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bx%5E2-16x%2B64-26=0 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx%5E2-16x%2B64-26=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 26 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-16x%2B38=0 ALIGN=MIDDLE  ALT=\"2x%5E2-16x%2B38=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for x:\r<BR>\n" );
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document.write( "Starting with the general quadratic\r<BR>\n" );
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document.write( "the general solution using the quadratic equation is:\r<BR>\n" );
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document.write( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax%5E2-16%2Ax%2B38=0 ALIGN=MIDDLE  ALT=\"2%2Ax%5E2-16%2Ax%2B38=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-16 ALIGN=MIDDLE  ALT=\"b=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=38 ALIGN=MIDDLE  ALT=\"c=38\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28--16+%2B-+sqrt%28+%28-16%29%5E2-4%2A2%2A38+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%28--16+%2B-+sqrt%28+%28-16%29%5E2-4%2A2%2A38+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=2, b=-16, and c=38\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2816+%2B-+sqrt%28+%28-16%29%5E2-4%2A2%2A38+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%2816+%2B-+sqrt%28+%28-16%29%5E2-4%2A2%2A38+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -16 to get 16\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2816+%2B-+sqrt%28+256-4%2A2%2A38+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%2816+%2B-+sqrt%28+256-4%2A2%2A38+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -16 to get 256  (note: remember when you square -16, you must square the negative as well. This is because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-16%29%5E2=-16%2A-16=256 ALIGN=MIDDLE  ALT=\"%28-16%29%5E2=-16%2A-16=256\"   DISABLED_style= \"max-width:90%; height:auto;\" >.)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2816+%2B-+sqrt%28+256%2B-304+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%2816+%2B-+sqrt%28+256%2B-304+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A38%2A2 ALIGN=MIDDLE  ALT=\"-4%2A38%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-304 ALIGN=MIDDLE  ALT=\"-304\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2816+%2B-+sqrt%28+-48+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%2816+%2B-+sqrt%28+-48+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2816+%2B-+4%2Ai%2Asqrt%283%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%2816+%2B-+4%2Ai%2Asqrt%283%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root (note: If you need help with simplifying the square root, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2816+%2B-+4%2Ai%2Asqrt%283%29%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x+=+%2816+%2B-+4%2Ai%2Asqrt%283%29%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 2 to get 4\r<BR>\n" );
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document.write( "After simplifying, the quadratic has roots of\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "Since we get a complex solution for the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-16x%2B38=0 ALIGN=MIDDLE  ALT=\"2x%5E2-16x%2B38=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that the equations <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2=26 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2=26\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x%2B8 ALIGN=MIDDLE  ALT=\"y=-x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > do not intersect. So there are no solutions </SPAN>\n" );
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