document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=422835>Question 422835</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve the equation in the complex number system <BR>\n" );
document.write( "8x^2+1=5x\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #295098 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=295098\">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=8x%5E2%2B1+=+5x ALIGN=MIDDLE  ALT=\"8x%5E2%2B1+=+5x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is a quadratic equation so we want one side to be zero. Subtracting 5x from each side we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%5E2-5x%2B1+=+0 ALIGN=MIDDLE  ALT=\"8x%5E2-5x%2B1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This won't factor so we'll use the Quadratic Formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2+-4%288%29%281%29%29%29%2F2%288%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2+-4%288%29%281%29%29%29%2F2%288%29\"   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=x+=+%28-%28-5%29+%2B-+sqrt%28+25+-4%288%29%281%29%29%29%2F2%288%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-5%29+%2B-+sqrt%28+25+-4%288%29%281%29%29%29%2F2%288%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-%28-5%29+%2B-+sqrt%28+25+-+32%29%29%2F2%288%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-5%29+%2B-+sqrt%28+25+-+32%29%29%2F2%288%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-%28-5%29+%2B-+sqrt%28-7%29%29%2F2%288%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-5%29+%2B-+sqrt%28-7%29%29%2F2%288%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+=+%285+%2B-+sqrt%28-7%29%29%2F16 ALIGN=MIDDLE  ALT=\"x+=+%285+%2B-+sqrt%28-7%29%29%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "With a negative number in the square root, we have complex solutions. To write our answers in standard form for complex numbers, a + bi, we start by factoring out -1:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%285+%2B-+sqrt%28-1%2A7%29%29%2F16 ALIGN=MIDDLE  ALT=\"x+=+%285+%2B-+sqrt%28-1%2A7%29%29%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%285+%2B-+sqrt%28-1%29%2Asqrt%287%29%29%2F16 ALIGN=MIDDLE  ALT=\"x+=+%285+%2B-+sqrt%28-1%29%2Asqrt%287%29%29%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-1%29+=+i ALIGN=MIDDLE  ALT=\"sqrt%28-1%29+=+i\"   DISABLED_style= \"max-width:90%; height:auto;\" > this becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%285+%2B-+i%2Asqrt%287%29%29%2F16 ALIGN=MIDDLE  ALT=\"x+=+%285+%2B-+i%2Asqrt%287%29%29%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now write the out the long way:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%285+%2B+i%2Asqrt%287%29%29%2F16 ALIGN=MIDDLE  ALT=\"x+=+%285+%2B+i%2Asqrt%287%29%29%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%285+-+i%2Asqrt%287%29%29%2F16 ALIGN=MIDDLE  ALT=\"x+=+%285+-+i%2Asqrt%287%29%29%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we split the fractions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+5%2F16+%2B+%28i%2Asqrt%287%29%29%2F16 ALIGN=MIDDLE  ALT=\"x+=+5%2F16+%2B+%28i%2Asqrt%287%29%29%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+5%2F16+%2B+%28-i%2Asqrt%287%29%29%2F16 ALIGN=MIDDLE  ALT=\"x+=+5%2F16+%2B+%28-i%2Asqrt%287%29%29%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which can be written as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+5%2F16+%2B+%28sqrt%287%29%2F16%29i ALIGN=MIDDLE  ALT=\"x+=+5%2F16+%2B+%28sqrt%287%29%2F16%29i\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+5%2F16+%2B+%28-sqrt%287%29%2F16%29i ALIGN=MIDDLE  ALT=\"x+=+5%2F16+%2B+%28-sqrt%287%29%2F16%29i\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "These are the complex solutions written in standard form. </SPAN>\n" );
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