document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=128762>Question 128762</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do I solve - <BR>\n" );
document.write( "x2 - 6x + 16 = 0<BR>\n" );
document.write( "It says there are no real answers, but that there are complex answers. What does this mean please?<BR>\n" );
document.write( "Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #94198 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=94198\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 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=x%5E2-6%2Ax%2B16=0 ALIGN=MIDDLE  ALT=\"x%5E2-6%2Ax%2B16=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-6 ALIGN=MIDDLE  ALT=\"b=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=16 ALIGN=MIDDLE  ALT=\"c=16\"   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--6+%2B-+sqrt%28+%28-6%29%5E2-4%2A1%2A16+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%28--6+%2B-+sqrt%28+%28-6%29%5E2-4%2A1%2A16+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=1, b=-6, and c=16\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%2A1%2A16+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%2A1%2A16+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -6 to get 6\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%286+%2B-+sqrt%28+36-4%2A1%2A16+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%286+%2B-+sqrt%28+36-4%2A1%2A16+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -6 to get 36  (note: remember when you square -6, you must square the negative as well. This is because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-6%29%5E2=-6%2A-6=36 ALIGN=MIDDLE  ALT=\"%28-6%29%5E2=-6%2A-6=36\"   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+=+%286+%2B-+sqrt%28+36%2B-64+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%286+%2B-+sqrt%28+36%2B-64+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A16%2A1 ALIGN=MIDDLE  ALT=\"-4%2A16%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-64 ALIGN=MIDDLE  ALT=\"-64\"   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+=+%286+%2B-+sqrt%28+-28+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%286+%2B-+sqrt%28+-28+%29%29%2F%282%2A1%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+=+%286+%2B-+2%2Ai%2Asqrt%287%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%286+%2B-+2%2Ai%2Asqrt%287%29%29%2F%282%2A1%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+=+%286+%2B-+2%2Ai%2Asqrt%287%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%286+%2B-+2%2Ai%2Asqrt%287%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 1 to get 2\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( "Notice if we graph the quadratic <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2-6%2Ax%2B16 ALIGN=MIDDLE  ALT=\"y=x%5E2-6%2Ax%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-12%2C+18%2C+-8%2C+22%2C+x%5E2-6%2Ax%2B16%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-12%2C+18%2C+-8%2C+22%2C+x%5E2-6%2Ax%2B16%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2-6%2Ax%2B16 ALIGN=MIDDLE  ALT=\"y=x%5E2-6%2Ax%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And we can see that there are no real roots\r<BR>\n" );
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