document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=785546>Question 785546</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the equation for x:  (7x+1)^2+(15x+2)^2=(17x+1)^2\r<BR>\n" );
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document.write( "My answer: (7x)^2+2*7x*1+1^2+(15x)^2+2*15x*2+2^2=(17x)^2+2*17x*1+1^2<BR>\n" );
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document.write( "            49x^2+14x+1+225x^2+60x+4=289x^2+34x+1=\r<BR>\n" );
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document.write( "             274x^2+74x+5=289x^2+34x+1<BR>\n" );
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document.write( "             74x+5=15x^2+34x+1<BR>\n" );
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document.write( "              40x+5=15x^2+1\r<BR>\n" );
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document.write( "               40x=15x^2-4\r<BR>\n" );
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document.write( "                 x=15x^2-4/40\r<BR>\n" );
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document.write( "Austrian Math 8th grade. I can't seem to find the answer. 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 #477601 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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/cgi-bin/show-face.mpl?user=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=477601\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 7x+1)^2+(15x+2)^2=(17x+1)^2\r<BR>\n" );
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document.write( "My answer: (7x)^2+2*7x*1+1^2+(15x)^2+2*15x*2+2^2=(17x)^2+2*17x*1+1^2<BR>\n" );
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document.write( "            49x^2+14x+1+225x^2+60x+4=289x^2+34x+1=\r<BR>\n" );
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document.write( "             274x^2+74x+5=289x^2+34x+1<BR>\n" );
document.write( "             <BR>\n" );
document.write( "             74x+5=15x^2+34x+1<BR>\n" );
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document.write( "              40x+5=15x^2+1\r<BR>\n" );
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document.write( "               40x=15x^2-4<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x%5E2+-+40x+-+4+=+0 ALIGN=MIDDLE  ALT=\"15x%5E2+-+40x+-+4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x%5E2%2B-40x%2B-4+=+0 ALIGN=MIDDLE  ALT=\"15x%5E2%2B-40x%2B-4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
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document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-40%29%5E2-4%2A15%2A-4=1840 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-40%29%5E2-4%2A15%2A-4=1840\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "  Discriminant d=1840 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--40%2B-sqrt%28+1840+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--40%2B-sqrt%28+1840+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28-40%29%2Bsqrt%28+1840+%29%29%2F2%5C15+=+2.76317403930181 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-40%29%2Bsqrt%28+1840+%29%29%2F2%5C15+=+2.76317403930181\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-40%29-sqrt%28+1840+%29%29%2F2%5C15+=+-0.0965073726351477 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-40%29-sqrt%28+1840+%29%29%2F2%5C15+=+-0.0965073726351477\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x%5E2%2B-40x%2B-4 ALIGN=MIDDLE  ALT=\"15x%5E2%2B-40x%2B-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x%5E2%2B-40x%2B-4+=+%28x-2.76317403930181%29%2A%28x--0.0965073726351477%29 ALIGN=MIDDLE  ALT=\"15x%5E2%2B-40x%2B-4+=+%28x-2.76317403930181%29%2A%28x--0.0965073726351477%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 2.76317403930181, -0.0965073726351477.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+15%2Ax%5E2%2B-40%2Ax%2B-4+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+15%2Ax%5E2%2B-40%2Ax%2B-4+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "============<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4%2F3+%2B+2sqrt%28115%29%2F15 ALIGN=MIDDLE  ALT=\"x+=+4%2F3+%2B+2sqrt%28115%29%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4%2F3+-+2sqrt%28115%29%2F15 ALIGN=MIDDLE  ALT=\"x+=+4%2F3+-+2sqrt%28115%29%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "                 x=15x^2-4/40<BR>\n" );
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