document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=190741>Question 190741</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This question is from a homework that was handed out in class.<BR>\n" );
document.write( "I don't understand the problem, please help me.<BR>\n" );
document.write( "Thanks\r<BR>\n" );
document.write( "\n" );
document.write( "Solve for x<BR>\n" );
document.write( "(x+4)^1/2 + 5x(x+4)^3/2 =0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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 #143213 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=143213\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (x+4)^1/2 + 5x(x+4)^3/2 =0 <BR>\n" );
document.write( ".<BR>\n" );
document.write( "Begin by factoring out (x+4)^1/2:<BR>\n" );
document.write( "(x+4)^1/2 [1 + 5x(x+4)^2/2] = 0<BR>\n" );
document.write( "(x+4)^1/2 [1 + 5x(x+4)] = 0<BR>\n" );
document.write( "(x+4)^1/2 [1 + 5x^2 + 20x] = 0<BR>\n" );
document.write( "(x+4)^1/2 [5x^2 + 20x + 1] = 0<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now, the problem is reduced to finding values of 'x' when:<BR>\n" );
document.write( "(x+4)^1/2 = 0<BR>\n" );
document.write( "and<BR>\n" );
document.write( "5x^2 + 20x + 1 = 0<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Top one:<BR>\n" );
document.write( "(x+4)^1/2 = 0<BR>\n" );
document.write( "(x+4) = 0<BR>\n" );
document.write( "x = -4<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Bottom one:<BR>\n" );
document.write( "5x^2 + 20x + 1 = 0<BR>\n" );
document.write( "Applying the quadratic equation yields two solutions:<BR>\n" );
document.write( "x = {-0.051, -3.949}<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Combined solutions, then are:<BR>\n" );
document.write( "x = {-0.051, -3.949, -4}<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Details of the quadratic follows:<BR>\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=5x%5E2%2B20x%2B1+=+0 ALIGN=MIDDLE  ALT=\"5x%5E2%2B20x%2B1+=+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=%2820%29%5E2-4%2A5%2A1=380 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2820%29%5E2-4%2A5%2A1=380\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=380 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+=+%28-20%2B-sqrt%28+380+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-20%2B-sqrt%28+380+%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-%2820%29%2Bsqrt%28+380+%29%29%2F2%5C5+=+-0.0506411310382074 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2820%29%2Bsqrt%28+380+%29%29%2F2%5C5+=+-0.0506411310382074\"   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-%2820%29-sqrt%28+380+%29%29%2F2%5C5+=+-3.94935886896179 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2820%29-sqrt%28+380+%29%29%2F2%5C5+=+-3.94935886896179\"   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=5x%5E2%2B20x%2B1 ALIGN=MIDDLE  ALT=\"5x%5E2%2B20x%2B1\"   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=5x%5E2%2B20x%2B1+=+5%28x--0.0506411310382074%29%2A%28x--3.94935886896179%29 ALIGN=MIDDLE  ALT=\"5x%5E2%2B20x%2B1+=+5%28x--0.0506411310382074%29%2A%28x--3.94935886896179%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -0.0506411310382074, -3.94935886896179.\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+5%2Ax%5E2%2B20%2Ax%2B1+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B20%2Ax%2B1+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );