document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170613>Question 1170613</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve for x: x^2= 3x-5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #795449 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=795449\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the equation is x^2 = 3x - 5\r<BR>\n" );
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document.write( "subtrct 3x from both sides of the equation and add 5 to both sides of the equation to get:\r<BR>\n" );
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document.write( "x^2 - 3x + 5 = 0.\r<BR>\n" );
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document.write( "use the quadratic equation to solve this quadratic equation to get:\r<BR>\n" );
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document.write( "the roots are:\r<BR>\n" );
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document.write( "z = 1.5 + 1.6583123951777i or x = 1.5 - 1.6583123951777i\r<BR>\n" );
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document.write( "those are the roots of the equation, which are complex numbers that contain an imaginary part because the equation does not cross the line y = 0.\r<BR>\n" );
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document.write( "if the roots were real, the graph of the equation would have cross the x-axis.\r<BR>\n" );
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document.write( "the x-axis is when the value of y on the graph is equal to 0.\r<BR>\n" );
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document.write( "the quadratic equation solves for the roots, even if they are not real.\r<BR>\n" );
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document.write( "a complex number has a real part and an imaginary part.\r<BR>\n" );
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document.write( "the real part is a real number.\r<BR>\n" );
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document.write( "the imaginary part is a real number times the letter i.\r<BR>\n" );
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document.write( "the letter i represents the square root of (-1).\r<BR>\n" );
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document.write( "here's a reference on complex numbers.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.mathsisfun.com/numbers/complex-numbers.html\" target = \"_blank\">https://www.mathsisfun.com/numbers/complex-numbers.html</a>\r<BR>\n" );
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document.write( "there are many more references on the web.<BR>\n" );
document.write( "just do a search for complex numbers.\r<BR>\n" );
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