document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=349708>Question 349708</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I just forgot how to do the algebra in this equation:\r<BR>\n" );
document.write( "\n" );
document.write( "    (x^2)<BR>\n" );
document.write( "  --------- = 49<BR>\n" );
document.write( "  (.4-x)^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #249958 by </B><A HREF=/tutors/aboutme.mpl?userid=CharlesG2><B>CharlesG2(834)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CharlesG2><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=249958\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I just forgot how to do the algebra in this equation:\r<BR>\n" );
document.write( "\n" );
document.write( "    (x^2)<BR>\n" );
document.write( "  --------- = 49<BR>\n" );
document.write( "  (.4-x)^2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x^2 = 49 * (.4 - x)^2 (multiplied both sides by (.4 - x)^2)<BR>\n" );
document.write( "x^2 = 49 * (.4 - x) * (.4 - x) (expanded the (.4 - x)^2)<BR>\n" );
document.write( "x^2 = 49 * (.4^2 - .4x - .4x + x^2) (used FOIL, First Outer Inner Last)<BR>\n" );
document.write( "x^2 = 49 * (.16 - .8x + x^2) (simplified)<BR>\n" );
document.write( "x^2 = 49 * .16 - 49 * .8x + 49x^2 (distributed the 49 across)<BR>\n" );
document.write( "x^2 = 7.84 - 39.2x + 49x^2<BR>\n" );
document.write( "-49x^2 + x^2 + 39.2x - 7.84 = 0 (brought terms together and when putting terms to opposite side of equal sign changed sign on the terms)<BR>\n" );
document.write( "-48x^2 + 39.2x - 7.84 = 0 (simplified)<BR>\n" );
document.write( "48x^2 - 39.2x + 7.84 = 0 (divided both sides by -1)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if you want to solve for x, use the quadratic formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "in this case, a = 48, b = -39.2, c = 7.84\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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=48x%5E2%2B-39.2x%2B7.84+=+0 ALIGN=MIDDLE  ALT=\"48x%5E2%2B-39.2x%2B7.84+=+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=%28-39.2%29%5E2-4%2A48%2A7.84=31.3600000000004 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-39.2%29%5E2-4%2A48%2A7.84=31.3600000000004\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=31.3600000000004 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--39.2%2B-sqrt%28+31.3600000000004+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--39.2%2B-sqrt%28+31.3600000000004+%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-%28-39.2%29%2Bsqrt%28+31.3600000000004+%29%29%2F2%5C48+=+0.466666666666667 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-39.2%29%2Bsqrt%28+31.3600000000004+%29%29%2F2%5C48+=+0.466666666666667\"   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-%28-39.2%29-sqrt%28+31.3600000000004+%29%29%2F2%5C48+=+0.35 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-39.2%29-sqrt%28+31.3600000000004+%29%29%2F2%5C48+=+0.35\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48x%5E2%2B-39.2x%2B7.84 ALIGN=MIDDLE  ALT=\"48x%5E2%2B-39.2x%2B7.84\"   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=48x%5E2%2B-39.2x%2B7.84+=+48%28x-0.466666666666667%29%2A%28x-0.35%29 ALIGN=MIDDLE  ALT=\"48x%5E2%2B-39.2x%2B7.84+=+48%28x-0.466666666666667%29%2A%28x-0.35%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 0.466666666666667, 0.35.\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+48%2Ax%5E2%2B-39.2%2Ax%2B7.84+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+48%2Ax%5E2%2B-39.2%2Ax%2B7.84+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );