document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=641585>Question 641585</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve the equation  in real # system\r<BR>\n" );
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document.write( "real solutions of the equation are x=?\r<BR>\n" );
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document.write( "dont see why my tutor i was assigned cant do these, please help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #403742 by </B><A HREF=/tutors/aboutme.mpl?userid=MathTherapy><B>MathTherapy(10552)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathTherapy><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/cgi-bin/show-face.mpl?user=MathTherapy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=403742\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "solve the equation  in real # system\r<BR>\n" );
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document.write( "real solutions of the equation are x=?\r<BR>\n" );
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document.write( "dont see why my tutor i was assigned cant do these, please help\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E3+-+3x%5E2+%2B+31x+%2B+8+=+0 ALIGN=MIDDLE  ALT=\"4x%5E3+-+3x%5E2+%2B+31x+%2B+8+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---- Multiplying eq by 4 to clear the fractions\r<BR>\n" );
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document.write( "From calculations, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-+1%2F4 ALIGN=MIDDLE  ALT=\"-+1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > was found to be a root of the equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-+1%2F4 ALIGN=MIDDLE  ALT=\"x+=+-+1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+1%2F4+=+0 ALIGN=MIDDLE  ALT=\"x+%2B+1%2F4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----- 4x + 1 = 0.<BR>\n" );
document.write( "This means that one real solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-+1%2F4 ALIGN=MIDDLE  ALT=\"x+=+-+1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-+0.25 ALIGN=MIDDLE  ALT=\"-+0.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Using long division and dividing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E3+-+3x%5E2+%2B+31x+%2B+8 ALIGN=MIDDLE  ALT=\"4x%5E3+-+3x%5E2+%2B+31x+%2B+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > by 4x + 1, we get: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+x+%2B+8 ALIGN=MIDDLE  ALT=\"x%5E2+-+x+%2B+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We now have: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E3+-+3x%5E2+%2B+31x+%2B+8+=+0 ALIGN=MIDDLE  ALT=\"4x%5E3+-+3x%5E2+%2B+31x+%2B+8+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x+%2B+1%29%28x%5E2+-+x+%2B+8%29+=+0 ALIGN=MIDDLE  ALT=\"%284x+%2B+1%29%28x%5E2+-+x+%2B+8%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solving <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+x+%2B+8 ALIGN=MIDDLE  ALT=\"x%5E2+-+x+%2B+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > using the quadratic equation formula gives us a negative discriminant (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+-+4ac ALIGN=MIDDLE  ALT=\"b%5E2+-+4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >), or 1 – 4 * 1 * 8, or 1 – 32, or - 31)\r<BR>\n" );
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document.write( "As a negative discriminant gives us 2 imaginary solutions, both of which DO NOT INTERSECT the x-axis, the 2 imaginary solutions are regarded as non-solutions, since we're looking for real solutions.\r<BR>\n" );
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document.write( "Therefore, the one and only REAL solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28x+=+-+1%2F4%29 ALIGN=MIDDLE  ALT=\"highlight_green%28x+=+-+1%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28-+0.25%29 ALIGN=MIDDLE  ALT=\"highlight_green%28-+0.25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "I hope this helps you understand it better!!\r<BR>\n" );
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document.write( "Send comments and “thank-yous” to “D” at MathMadEzy@aol.com  </SPAN>\n" );
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