document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=88032>Question 88032</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve<BR>\n" );
document.write( "2x^2-5x=3\r<BR>\n" );
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document.write( "Having trouble..any help appreciated.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #63927 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=63927\">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=2+x+%5E+2+-+5+x+=+3+ ALIGN=MIDDLE  ALT=\"2+x+%5E+2+-+5+x+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+x+%5E+2+-+5+x+-+3+=+0+ ALIGN=MIDDLE  ALT=\"2+x+%5E+2+-+5+x+-+3+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 3 from both sides\r<BR>\n" );
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document.write( "Now let's use the quadratic formula to solve for x:\r<BR>\n" );
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document.write( "Starting with the general quadratic\r<BR>\n" );
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document.write( "the general form of the quadratic equation 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( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax%5E2-5%2Ax-3=0 ALIGN=MIDDLE  ALT=\"2%2Ax%5E2-5%2Ax-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-5 ALIGN=MIDDLE  ALT=\"b=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-3 ALIGN=MIDDLE  ALT=\"c=-3\"   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+%2B-+sqrt%28+%28-5%29%5E2-4%2A2%2A-3+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%2A2%2A-3+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=2, b=-5, and c=-3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%285+%2B-+sqrt%28+25-4%2A2%2A-3+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%285+%2B-+sqrt%28+25-4%2A2%2A-3+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -5 to get 25\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%285+%2B-+sqrt%28+25%2B24+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%285+%2B-+sqrt%28+25%2B24+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A-3%2A2 ALIGN=MIDDLE  ALT=\"-4%2A-3%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24 ALIGN=MIDDLE  ALT=\"24\"   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+%2B-+sqrt%28+49+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%285+%2B-+sqrt%28+49+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%285+%2B-+7%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%285+%2B-+7%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%285+%2B-+7%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%285+%2B-+7%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 2 to get 4\r<BR>\n" );
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document.write( "So now the expression breaks down into two parts\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%285+%2B+7%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%285+%2B+7%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%285+-+7%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%285+-+7%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Lets look at the first part:\r<BR>\n" );
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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;\" > Add the terms in the numerator\r<BR>\n" );
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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;\" > Divide\r<BR>\n" );
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document.write( "So one answer is\r<BR>\n" );
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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;\" >\r<BR>\n" );
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document.write( "Now lets look at the second part:\r<BR>\n" );
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document.write( "<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;\" > Subtract the terms in the numerator\r<BR>\n" );
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document.write( "<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;\" > Divide\r<BR>\n" );
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document.write( "So another answer is\r<BR>\n" );
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document.write( "So our solutions are:\r<BR>\n" );
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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( "Notice when we graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax%5E2-5%2Ax-3 ALIGN=MIDDLE  ALT=\"2%2Ax%5E2-5%2Ax-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-11%2C+13%2C+-11%2C+13%2C2%2Ax%5E2%2B-5%2Ax%2B-3%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-11%2C+13%2C+-11%2C+13%2C2%2Ax%5E2%2B-5%2Ax%2B-3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and we can see that the roots are <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;\" > and <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;\" >. This verifies our answer </SPAN>\n" );
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