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 #153935 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=153935\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ok, you are good up to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%288%2B-sqrt%28124%29%29%2F10 ALIGN=MIDDLE  ALT=\"x+=+%288%2B-sqrt%28124%29%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now you factor the 124 under the radical into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28124%29+=+sqrt%284%2A31%29 ALIGN=MIDDLE  ALT=\"sqrt%28124%29+=+sqrt%284%2A31%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the purpose of this step is to see if the radicand (the quantity under the radical) has any factors that are perfect squares. In this case, there is a factor of 4 which is a perfect square and can be moved out from under the radical by taking its square root, since:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%29+=+2 ALIGN=MIDDLE  ALT=\"sqrt%284%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so we get the next step:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%288%2B2%2Asqrt%2831%29%29%2F10 ALIGN=MIDDLE  ALT=\"x+=+%288%2B2%2Asqrt%2831%29%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%288-2%2Asqrt%2831%29%29%2F10 ALIGN=MIDDLE  ALT=\"x+=+%288-2%2Asqrt%2831%29%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Notice that we can factor out a 2 in the numerator and also in the denominator.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28cross%282%29%284%2Bsqrt%2831%29%29%29%2Fcross%282%29%285%29 ALIGN=MIDDLE  ALT=\"x+=+%28cross%282%29%284%2Bsqrt%2831%29%29%29%2Fcross%282%29%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28cross%282%29%284-sqrt%2831%29%29%29%2Fcross%282%29%285%29 ALIGN=MIDDLE  ALT=\"x+=+%28cross%282%29%284-sqrt%2831%29%29%29%2Fcross%282%29%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cancel the 2's to leave you with:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x+=+%284%2B-sqrt%2831%29%29%2F5%29 ALIGN=MIDDLE  ALT=\"highlight%28x+=+%284%2B-sqrt%2831%29%29%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );