document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=107041>Question 107041</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i need help solving these quadratic equations using the quadratic formula.<BR>\n" );
document.write( "2x^2 - 5x = 3\r<BR>\n" );
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document.write( "3x^2 - 2x + 1 = 0<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #77871 by </B><A HREF=/tutors/aboutme.mpl?userid=HyperBrain><B>HyperBrain(694)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=HyperBrain><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=77871\">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=2x%5E2-5x=3 ALIGN=MIDDLE  ALT=\"2x%5E2-5x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-5x-3=3-3 ALIGN=MIDDLE  ALT=\"2x%5E2-5x-3=3-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-5x-3=0 ALIGN=MIDDLE  ALT=\"2x%5E2-5x-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The quadratic formula for solving the value of x in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Here, a=2, b=-5, and c=-3.So,\r<BR>\n" );
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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%2A2%2A%28-3%29%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x=%28-%28-5%29%2B-sqrt%28%28-5%29%5E2-4%2A2%2A%28-3%29%29%29%2F%282%2A2%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%2825-%28-24%29%29%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x=%285%2B-sqrt%2825-%28-24%29%29%29%2F%284%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%2825%2B24%29%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x=%285%2B-sqrt%2825%2B24%29%29%2F%284%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%2849%29%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x=%285%2B-sqrt%2849%29%29%2F%284%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-+7%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x=%285%2B-+7%29%2F%284%29\"   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=%285%2B7%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x=%285%2B7%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%285-7%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x=%285-7%29%2F%284%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=12%2F4 ALIGN=MIDDLE  ALT=\"x=12%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2%2F4 ALIGN=MIDDLE  ALT=\"x=-2%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1%2F2 ALIGN=MIDDLE  ALT=\"x=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "For your next problem, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+-2x%2B1+=+0 ALIGN=MIDDLE  ALT=\"3x%5E2+-2x%2B1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Here, a=3, b=-2, c=1.\r<BR>\n" );
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document.write( "Using the quadratic formula,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-%28-2%29%2B-sqrt%28%28-2%29%5E2-4%2A3%2A1%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x=%28-%28-2%29%2B-sqrt%28%28-2%29%5E2-4%2A3%2A1%29%29%2F%282%2A3%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=%282%2B-sqrt%284-12%29%29%2F%286%29 ALIGN=MIDDLE  ALT=\"x=%282%2B-sqrt%284-12%29%29%2F%286%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=%282%2B-sqrt%28-8%29%29%2F%286%29 ALIGN=MIDDLE  ALT=\"x=%282%2B-sqrt%28-8%29%29%2F%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We know that square root of a negative number does not exist because all squares are positive numbers. In this cases, oftentimes, mathematicians use the symbol <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i ALIGN=MIDDLE  ALT=\"i\"   DISABLED_style= \"max-width:90%; height:auto;\" > for the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's continue\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%282%2B-sqrt%28%28-1%29%284%29%282%29%29%29%2F%286%29 ALIGN=MIDDLE  ALT=\"x=%282%2B-sqrt%28%28-1%29%284%29%282%29%29%29%2F%286%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=%282%2B-+%28sqrt%28-1%29%29%28sqrt%284%29%29%28sqrt%282%29%29%29%2F%286%29 ALIGN=MIDDLE  ALT=\"x=%282%2B-+%28sqrt%28-1%29%29%28sqrt%284%29%29%28sqrt%282%29%29%29%2F%286%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=%282%2B-+%28i%29%282%29%28sqrt%282%29%29%29%2F%286%29 ALIGN=MIDDLE  ALT=\"x=%282%2B-+%28i%29%282%29%28sqrt%282%29%29%29%2F%286%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=%282%2B-+2i+%28sqrt%282%29%29%29%2F%286%29 ALIGN=MIDDLE  ALT=\"x=%282%2B-+2i+%28sqrt%282%29%29%29%2F%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Roots involving <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i ALIGN=MIDDLE  ALT=\"i\"   DISABLED_style= \"max-width:90%; height:auto;\" > are called imaginary roots.\r<BR>\n" );
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document.write( "Power up,<BR>\n" );
document.write( "HyperBrain!<BR>\n" );
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