document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=204020>Question 204020</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with one part of solution when using the quadratic formula. My textbook does not explain this part. I will list up to where I begin to get confused.\r<BR>\n" );
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document.write( "Solve: 5x^2-8x-3=0\r<BR>\n" );
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document.write( "a=5, b=-8. c=-3\r<BR>\n" );
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document.write( "-(-8)+/- sqrt(-8)^2-4(5)(-3) divided by 2(5)\r<BR>\n" );
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document.write( "8 +/- sqrt64+60 divided by 10\r<BR>\n" );
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document.write( "8 +/- sqrt124 divided by 10\r<BR>\n" );
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document.write( "this is where it gets confusing:<BR>\n" );
document.write( "8+/- sqrt (4) (31) divided by 10\r<BR>\n" );
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document.write( "8+/- 2 sqrt31 divided by 10 =2(4+/- sqrt31 divided by (2)(5)\r<BR>\n" );
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document.write( "= 2/2 times 4+/- sqrt31 divided by 5 = 4+/-sqrt31 divided by 5\r<BR>\n" );
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document.write( "I do not understand what is happening during this part. Please walk me through and explain what is being done and why it is done.  thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153932 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=153932\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll start where you're starting to get confused\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%288%2B-sqrt%28124%29%29%2F%2810%29 ALIGN=MIDDLE  ALT=\"x=%288%2B-sqrt%28124%29%29%2F%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "The goal now is to simplify the right side any way we can. It turns out that the square root can be simplified.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%288%2B-sqrt%284%2A31%29%29%2F%2810%29 ALIGN=MIDDLE  ALT=\"x=%288%2B-sqrt%284%2A31%29%29%2F%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor 124 into 4*31. Note: 4*31=124. \r<BR>\n" );
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document.write( "Why did we do this? Because when we break up the root, we can take the square root of 4 to get 2...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%288%2B-sqrt%284%29%2Asqrt%2831%29%29%2F%2810%29 ALIGN=MIDDLE  ALT=\"x=%288%2B-sqrt%284%29%2Asqrt%2831%29%29%2F%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up 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=%288+%2B-+2%2Asqrt%2831%29%29%2F%2810%29 ALIGN=MIDDLE  ALT=\"x=%288+%2B-+2%2Asqrt%2831%29%29%2F%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of 4 to get 2.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%282%284%2B-sqrt%2831%29%29%29%2F%2810%29 ALIGN=MIDDLE  ALT=\"x=%282%284%2B-sqrt%2831%29%29%29%2F%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF 2 from the numerator.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%282%284%2B-sqrt%2831%29%29%29%2F%282%2A5%29 ALIGN=MIDDLE  ALT=\"x=%282%284%2B-sqrt%2831%29%29%29%2F%282%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the denominator 10 to get 2*5\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28highlight%282%29%284%2B-sqrt%2831%29%29%29%2F%28highlight%282%29%2A5%29 ALIGN=MIDDLE  ALT=\"x=%28highlight%282%29%284%2B-sqrt%2831%29%29%29%2F%28highlight%282%29%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Highlight the common terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28cross%282%29%284%2B-sqrt%2831%29%29%29%2F%28cross%282%29%2A5%29 ALIGN=MIDDLE  ALT=\"x=%28cross%282%29%284%2B-sqrt%2831%29%29%29%2F%28cross%282%29%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cancel out the common terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%284%2B-sqrt%2831%29%29%2F5 ALIGN=MIDDLE  ALT=\"x=%284%2B-sqrt%2831%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "So the solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%284%2Bsqrt%2831%29%29%2F5 ALIGN=MIDDLE  ALT=\"x=%284%2Bsqrt%2831%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%284-sqrt%2831%29%29%2F5 ALIGN=MIDDLE  ALT=\"x=%284-sqrt%2831%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (since the 'plus/minus' breaks the equation in two).\r<BR>\n" );
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document.write( "Note: I showed more steps than you would necessarily show to illustrate what is really going on. </SPAN>\n" );
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