document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1118951>Question 1118951</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve each of the following quadratic equations using Quadratic Formula with answer in imaginary value.\r<BR>\n" );
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document.write( "1. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2-2x%2B5 ALIGN=MIDDLE  ALT=\"4x%5E2-2x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B2x-6 ALIGN=MIDDLE  ALT=\"2x%5E2%2B2x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I got:<BR>\n" );
document.write( "1. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2B2sqrt%28-19%29%29%2F8 ALIGN=MIDDLE  ALT=\"%282%2B2sqrt%28-19%29%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282-2sqrt%28-19%29%29%2F8 ALIGN=MIDDLE  ALT=\"%282-2sqrt%28-19%29%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2B1sqrt%2813%29%29%2F2 ALIGN=MIDDLE  ALT=\"%28-1%2B1sqrt%2813%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1-1sqrt%2813%29%29%2F2 ALIGN=MIDDLE  ALT=\"%28-1-1sqrt%2813%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "How do I proceed? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #734364 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=734364\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sqrt(-19) is equal to sqrt(19 * -1).\r<BR>\n" );
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document.write( "sqrt(-1) is equal to i.\r<BR>\n" );
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document.write( "therefore, sqrt(-19) is equal to i * sqrt(19).\r<BR>\n" );
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document.write( "this is equal to sqrt(-1) * sqrt(19) which is equal to sqrt(-19).\r<BR>\n" );
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document.write( "in place of sqrt(-19), use sqrt(19) * i\r<BR>\n" );
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document.write( "number 2 doesn't have an imaginary part since the number under your sqrt sign is positive.\r<BR>\n" );
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document.write( "your answer to 1 would be:\r<BR>\n" );
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document.write( "(2 + 2 * sqrt(19) * i) / 8 which your would simplify to .25 plus or minus 1.089724736 * i\r<BR>\n" );
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document.write( "that's what the quadratic equation solver i used got, so it looks good when you take into account rounding.\r<BR>\n" );
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document.write( "the quadratic equation solver i used got:\r<BR>\n" );
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document.write( "x = 0.25 + 1.0897247358852i or x = 0.25 - 1.0897247358852i\r<BR>\n" );
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document.write( "the quadratic solver gave me x = -2.302775637732 or x = 1.302775637732\r<BR>\n" );
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document.write( "your solution was x = (-1 plus or minus sqrt(13)) / 2.\r<BR>\n" );
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document.write( "this simplifies to x = -2.302775638 or x = 1.302775638.\r<BR>\n" );
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document.write( "same answer if you take into account rounding.\r<BR>\n" );
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document.write( "rules for imaginary numbers.\r<BR>\n" );
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document.write( "sqrt(-1) = i\r<BR>\n" );
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document.write( "sqrt(-1)^2 = -1\r<BR>\n" );
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document.write( "sqrt(-1)^3 = -i\r<BR>\n" );
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document.write( "sqrt(-1)^4 = 1\r<BR>\n" );
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document.write( "it repeats this for every sets of 4 exonents.\r<BR>\n" );
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document.write( "here's a reference.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.mathsisfun.com/numbers/imaginary-numbers.html\" target = \"_blank\">https://www.mathsisfun.com/numbers/imaginary-numbers.html</a>\r<BR>\n" );
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document.write( "the quadratic equation solver i used can be found at <a  rel=nofollow HREF= \"https://www.mathsisfun.com/quadratic-equation-solver.html\" target = \"_blank\">https://www.mathsisfun.com/quadratic-equation-solver.html</a> </SPAN>\n" );
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