document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=548842>Question 548842</A>: <I><SPAN STYLE=\"word-break: break-all;\"> show me how to solve this equation 2(x-8)^ 2+x^2=x(x=51)-43x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #357234 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=357234\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2*(x-8)^2 +x^2 = x*(x-51) - 43*x<BR>\n" );
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document.write( "Use FOIL to expand the second term.<BR>\n" );
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document.write( "2*(x^2-16x+64) +x^2 = x*(x-51) - 43*x<BR>\n" );
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document.write( "Use the distributive property to eliminate the parentheses.<BR>\n" );
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document.write( "2x^2 -32x + 128 +x^2 = x^2 -51x - 43x<BR>\n" );
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document.write( "Collect terms<BR>\n" );
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document.write( "3x^2 -32x + 128 = x^2 -94x<BR>\n" );
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document.write( "Subtract x^2 from both sides<BR>\n" );
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document.write( "2x^2 -32x + 128 = -94x<BR>\n" );
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document.write( "Add 94x to both sides<BR>\n" );
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document.write( "2x^2 +62x + 128 = 0<BR>\n" );
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document.write( "Divide both sides by 2<BR>\n" );
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document.write( "x^2 +31x + 64 = 0<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=quadratic.solver>SOLVE quadratic equation with variable</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=1x%5E2%2B31x%2B64+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B31x%2B64+=+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" );
document.write( "  <BR>\n" );
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" );
document.write( "  <BR>\n" );
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=%2831%29%5E2-4%2A1%2A64=705 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2831%29%5E2-4%2A1%2A64=705\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=705 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+=+%28-31%2B-sqrt%28+705+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-31%2B-sqrt%28+705+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%2831%29%2Bsqrt%28+705+%29%29%2F2%5C1+=+-2.22408195264825 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2831%29%2Bsqrt%28+705+%29%29%2F2%5C1+=+-2.22408195264825\"   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-%2831%29-sqrt%28+705+%29%29%2F2%5C1+=+-28.7759180473518 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2831%29-sqrt%28+705+%29%29%2F2%5C1+=+-28.7759180473518\"   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=1x%5E2%2B31x%2B64 ALIGN=MIDDLE  ALT=\"1x%5E2%2B31x%2B64\"   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=1x%5E2%2B31x%2B64+=+1%28x--2.22408195264825%29%2A%28x--28.7759180473518%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B31x%2B64+=+1%28x--2.22408195264825%29%2A%28x--28.7759180473518%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -2.22408195264825, -28.7759180473518.\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+1%2Ax%5E2%2B31%2Ax%2B64+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B31%2Ax%2B64+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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