document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=627563>Question 627563</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve the equation: 1/2(6+4x)-1/4(8x-12)=1/2(2x-4) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #395050 by </B><A HREF=/tutors/aboutme.mpl?userid=Maths68><B>Maths68(1474)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Maths68><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=Maths68><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=395050\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2%286%2B4x%29-1%2F4%288x-12%29=1%2F2%282x-4%29 ALIGN=MIDDLE  ALT=\"1%2F2%286%2B4x%29-1%2F4%288x-12%29=1%2F2%282x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%282%29%282%29%283%2B2x%29-1%2F%284%29%284%29%282x-3%29=1%2F%282%29%282%29%28x-2%29 ALIGN=MIDDLE  ALT=\"1%2F%282%29%282%29%283%2B2x%29-1%2F%284%29%284%29%282x-3%29=1%2F%282%29%282%29%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4%283%2B2x%29-1%2F16%282x-3%29=1%2F4%28x-2%29 ALIGN=MIDDLE  ALT=\"1%2F4%283%2B2x%29-1%2F16%282x-3%29=1%2F4%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply by 4 both sides\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%281%2F4%283%2B2x%29%29-4%281%2F16%282x-3%29%29=4%281%2F4%28x-2%29%29 ALIGN=MIDDLE  ALT=\"4%281%2F4%283%2B2x%29%29-4%281%2F16%282x-3%29%29=4%281%2F4%28x-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%284%29%281%2Fcross%284%29%283%2B2x%29%29-cross%284%29%281%2Fcross%2816%29%282x-3%29%29=cross%284%29%281%2Fcross%284%29%28x-2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%283%2B2x%29-1%2F4%282x-3%29=1%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"1%2F%283%2B2x%29-1%2F4%282x-3%29=1%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Take LCD<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%282x-3%29-%283%2B2x%29%29%2F%284%283%2B2x%29%282x-3%29%29=1%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"%284%282x-3%29-%283%2B2x%29%29%2F%284%283%2B2x%29%282x-3%29%29=1%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288x-12-3-2x%29%2F%284%283%2B2x%29%282x-3%29%29=1%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"%288x-12-3-2x%29%2F%284%283%2B2x%29%282x-3%29%29=1%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286x-15%29%2F%284%283%2B2x%29%282x-3%29%29=1%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"%286x-15%29%2F%284%283%2B2x%29%282x-3%29%29=1%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286x-15%29%28x-2%29=%281%29%284%29%283%2B2x%29%282x-3%29 ALIGN=MIDDLE  ALT=\"%286x-15%29%28x-2%29=%281%29%284%29%283%2B2x%29%282x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2-12x-15x%2B30=4%286x-9%2B4x%5E2-6x%29 ALIGN=MIDDLE  ALT=\"6x%5E2-12x-15x%2B30=4%286x-9%2B4x%5E2-6x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2-27x%2B30=4%28cross%286x%29-9%2B4x%5E2-cross%286x%29%29 ALIGN=MIDDLE  ALT=\"6x%5E2-27x%2B30=4%28cross%286x%29-9%2B4x%5E2-cross%286x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2-27x%2B30=4%28-9%2B4x%5E2%29 ALIGN=MIDDLE  ALT=\"6x%5E2-27x%2B30=4%28-9%2B4x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2-27x%2B30=-36%2B16x%5E2 ALIGN=MIDDLE  ALT=\"6x%5E2-27x%2B30=-36%2B16x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2-27x%2B30%2B36-16x%5E2=0 ALIGN=MIDDLE  ALT=\"6x%5E2-27x%2B30%2B36-16x%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2-16x%5E2-27x%2B30%2B36=0 ALIGN=MIDDLE  ALT=\"6x%5E2-16x%5E2-27x%2B30%2B36=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10x%5E2-27x%2B66=0 ALIGN=MIDDLE  ALT=\"-10x%5E2-27x%2B66=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply by -1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x%5E2%2B27x-66=0 ALIGN=MIDDLE  ALT=\"10x%5E2%2B27x-66=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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=10x%5E2%2B27x%2B-66+=+0 ALIGN=MIDDLE  ALT=\"10x%5E2%2B27x%2B-66+=+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=%2827%29%5E2-4%2A10%2A-66=3369 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2827%29%5E2-4%2A10%2A-66=3369\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=3369 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+=+%28-27%2B-sqrt%28+3369+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-27%2B-sqrt%28+3369+%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-%2827%29%2Bsqrt%28+3369+%29%29%2F2%5C10+=+1.55215437218629 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2827%29%2Bsqrt%28+3369+%29%29%2F2%5C10+=+1.55215437218629\"   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-%2827%29-sqrt%28+3369+%29%29%2F2%5C10+=+-4.25215437218629 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2827%29-sqrt%28+3369+%29%29%2F2%5C10+=+-4.25215437218629\"   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=10x%5E2%2B27x%2B-66 ALIGN=MIDDLE  ALT=\"10x%5E2%2B27x%2B-66\"   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=10x%5E2%2B27x%2B-66+=+10%28x-1.55215437218629%29%2A%28x--4.25215437218629%29 ALIGN=MIDDLE  ALT=\"10x%5E2%2B27x%2B-66+=+10%28x-1.55215437218629%29%2A%28x--4.25215437218629%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 1.55215437218629, -4.25215437218629.\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+10%2Ax%5E2%2B27%2Ax%2B-66+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+10%2Ax%5E2%2B27%2Ax%2B-66+%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" );