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 #153934 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=153934\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this is where it gets confusing:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288+%2B-+sqrt%28124%29%29%2F10 ALIGN=MIDDLE  ALT=\"%288+%2B-+sqrt%28124%29%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The next step is simplifying the square root. Simplifying square roots is done by finding perfect square factors of the radicand (the number inside the square root), if possible. The largest perfect square factor in 124 is 4. So we can rewrite 124 as 4*31:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288+%2B-+sqrt%284%2A31%29%29%2F10 ALIGN=MIDDLE  ALT=\"%288+%2B-+sqrt%284%2A31%29%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then we can use a property of square roots, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%2Ab%29+=+sqrt%28a%29%2Asqrt%28b%29 ALIGN=MIDDLE  ALT=\"sqrt%28a%2Ab%29+=+sqrt%28a%29%2Asqrt%28b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to split apart the two factors:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288+%2B-+sqrt%284%29%2Asqrt%2831%29%29%2F10 ALIGN=MIDDLE  ALT=\"%288+%2B-+sqrt%284%29%2Asqrt%2831%29%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we can simplify square root of the perfect square:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288+%2B-+2%2Asqrt%2831%29%29%2F10 ALIGN=MIDDLE  ALT=\"%288+%2B-+2%2Asqrt%2831%29%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The only thing left to do is reduce the fraction. This is done, as always, by finding common factors which will cancel. In this case 2 is a factor of both the numerator and denominator. So if we factor it out we can cancel them:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%284+%2B-+sqrt%2831%29%29%29%2F%282%2A5%29 ALIGN=MIDDLE  ALT=\"%282%284+%2B-+sqrt%2831%29%29%29%2F%282%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now the 2's cancel leaving:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284+%2B-+sqrt%2831%29%29%2F5 ALIGN=MIDDLE  ALT=\"%284+%2B-+sqrt%2831%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );