document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=409321>Question 409321</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I am having trouble solving quadratic equations.  I get down to the bottom of the problem and do not know how to reduce, or I do not get a perfect square because i made an error somewhere.  Would you please look at my work and help me?<BR>\n" );
document.write( "Solving by -b sqrt (b^2-4ac)/(2a)\r<BR>\n" );
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document.write( "20y^2+17y-10=0<BR>\n" );
document.write( "x= -17 sqrt ((17)^2-4(20(-10)/(2(20))\r<BR>\n" );
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document.write( "x = -17 sqrt +-(289-(-800))/(40)<BR>\n" );
document.write( "x = -17 sqrt +-(1089)/(40)<BR>\n" );
document.write( "x = -17 sqrt +- ((9)(121))/(40)<BR>\n" );
document.write( "x = -17 3 sqrt+- (121)/(40)  What to do here?\r<BR>\n" );
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document.write( "thanks\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #288245 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=288245\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are pretty close. Other than not finishing, the only mistake is that your \"+-\" is in the wrong place. It belongs in front of the square root. The Quadratic Formula is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28b%5E2-4ac%29%29%2F2a ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28b%5E2-4ac%29%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "With the \"+-\" in the right place, you are totally correct up to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-17+%2B-+sqrt%28%289%29%28121%29%29%29%2F40 ALIGN=MIDDLE  ALT=\"x+=+%28-17+%2B-+sqrt%28%289%29%28121%29%29%29%2F40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Next we use a property of radicals, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%28a%2C+p%2Aq%29+=+root%28a%2C+p%29%2Aroot%28a%2C+q%29 ALIGN=MIDDLE  ALT=\"root%28a%2C+p%2Aq%29+=+root%28a%2C+p%29%2Aroot%28a%2C+q%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to split the square root of the product into the product of the square roots of the factors:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-17+%2B-+sqrt%289%29%2Asqrt%28121%29%29%2F40 ALIGN=MIDDLE  ALT=\"x+=+%28-17+%2B-+sqrt%289%29%2Asqrt%28121%29%29%2F40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now, just like you had, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%289%29+=+3 ALIGN=MIDDLE  ALT=\"sqrt%289%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. What you didn't realize is that 121 is also a perfect square! <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%5E2+=+121 ALIGN=MIDDLE  ALT=\"11%5E2+=+121\"   DISABLED_style= \"max-width:90%; height:auto;\" > so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28121%29+=+11 ALIGN=MIDDLE  ALT=\"sqrt%28121%29+=+11\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Replacing these square roots with these whole numbers we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-17+%2B-+3%2A11%29%2F40 ALIGN=MIDDLE  ALT=\"x+=+%28-17+%2B-+3%2A11%29%2F40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplifies to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-17+%2B-+33%29%2F40 ALIGN=MIDDLE  ALT=\"x+=+%28-17+%2B-+33%29%2F40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is as far was we can go with the \"+-\". Next we write this \"the long way\":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-17+%2B+33%29%2F40 ALIGN=MIDDLE  ALT=\"x+=+%28-17+%2B+33%29%2F40\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-17+-+33%29%2F40 ALIGN=MIDDLE  ALT=\"x+=+%28-17+-+33%29%2F40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplifying each we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+16%2F40 ALIGN=MIDDLE  ALT=\"x+=+16%2F40\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-40%29%2F40 ALIGN=MIDDLE  ALT=\"x+=+%28-40%29%2F40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2%2F5 ALIGN=MIDDLE  ALT=\"x+=+2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-1 ALIGN=MIDDLE  ALT=\"x+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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